A Connection Between Elementary Functions and Higher Transcendental Functions
If f is holomorphic on a domain D in the complex plane, an analogous function F of several complex variables is constructed by taking a weighted average of f over the convex hull of {z1, z2, ⋯, zk}. Although F is defined at first only if the convex hull is contained in D, it is shown later that F ca...
Saved in:
| Published in: | SIAM journal on applied mathematics Vol. 17; no. 1; pp. 116 - 148 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.1969
|
| Subjects: | |
| ISSN: | 0036-1399, 1095-712X |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | If f is holomorphic on a domain D in the complex plane, an analogous function F of several complex variables is constructed by taking a weighted average of f over the convex hull of {z1, z2, ⋯, zk}. Although F is defined at first only if the convex hull is contained in D, it is shown later that F can be continued analytically along any rectifiable arc in Dk, provided that singular points with zi = zj (for some distinct i, j) are excluded if D is multiply connected. Taylor and Laurent series for f have single-series analogues for F, and the analogue of Cauchy's integral formula is a representation of F by an integral around a contour in D encircling z1, z2, ⋯, zk. The hypergeometric function 2F1(a, b; c; x) is an average of z-a over the line segment joining 1 - x and 1, the confluent hypergeometric function 1F1(b; c; x) is an average of ez over the line segment joining x and 0, and elliptic integrals are averages of a half-odd-integral power of z over a triangle (or a quadrilateral for integrals of the third kind). The average of z-a in the case of k complex variables is the hypergeometric R-function, which appears in both the series and contour-integral representations of F. The parameters b and c in the 2F1 and 1F1 functions come from the weight function used in the averaging process. Even in the case of k variables the weight function is taken to have a rather special form, with the result that F always satisfies a system of Euler-Poisson partial differential equations. Connections with axially symmetric potential theory, fractional integration, and integral transforms are mentioned briefly. |
|---|---|
| AbstractList | If $\,f$ is holomorphic on a domain $D$ in the complex plane, an analogous function $F$ of several complex variables is constructed by taking a weighted average of $\,f$ over the convex hull of $\{ z_1 ,z_2 , \cdots ,z_k \}$. Although $F$ is defined at first only if the convex hull is contained in $D$, it is shown later that $F$ can be continued analytically along any rectifiable arc in $D^k $, provided that singular points with $z_i = z_j $ (for some distinct $i$, $j$) are excluded if $D$ is multiply connected. Taylor and Laurent series for $f$ have single-series analogues for $F$, and the analogue of Cauchy's integral formula is a representation of $F$ by an integral around a contour in $D$ encircling $z_1 ,z_2 , \cdots ,z_k $. The hypergeometric function _2 F_1 (a,b;c;x)$ is an average of $z^{ - a } $ over the line segment joining $1-x$ and 1, the confluent hypergeometric function _1 F_1 (b;c;x)$ is an average of $e^z $ over the line segment joining $x$ and 0, and elliptic integrals are averages of a half-odd-integral power of $z$ over a triangle (or a quadrilateral for integrals of the third kind). The average of $z^{ - a } $ in the case of $k$ complex variables is the hypergeometric $R$-function, which appears in both the series and contour-integral representations of $F$. The parameters $b$ and $c$ in the _2 F_1 $ and _1 F_1 $ functions come from the weight function used in the averaging process. Even in the case of $k$ variables the weight function is taken to have a rather special form, with the result that $F$ always satisfies a system of Euler-Poisson partial differential equations. Connections with axially symmetric potential theory, fractional integration, and integral transforms are mentioned briefly. If f is holomorphic on a domain D in the complex plane, an analogous function F of several complex variables is constructed by taking a weighted average of f over the convex hull of {z1, z2, ⋯, zk}. Although F is defined at first only if the convex hull is contained in D, it is shown later that F can be continued analytically along any rectifiable arc in Dk, provided that singular points with zi = zj (for some distinct i, j) are excluded if D is multiply connected. Taylor and Laurent series for f have single-series analogues for F, and the analogue of Cauchy's integral formula is a representation of F by an integral around a contour in D encircling z1, z2, ⋯, zk. The hypergeometric function 2F1(a, b; c; x) is an average of z-a over the line segment joining 1 - x and 1, the confluent hypergeometric function 1F1(b; c; x) is an average of ez over the line segment joining x and 0, and elliptic integrals are averages of a half-odd-integral power of z over a triangle (or a quadrilateral for integrals of the third kind). The average of z-a in the case of k complex variables is the hypergeometric R-function, which appears in both the series and contour-integral representations of F. The parameters b and c in the 2F1 and 1F1 functions come from the weight function used in the averaging process. Even in the case of k variables the weight function is taken to have a rather special form, with the result that F always satisfies a system of Euler-Poisson partial differential equations. Connections with axially symmetric potential theory, fractional integration, and integral transforms are mentioned briefly. |
| Author | Carlson, B. C. |
| Author_xml | – sequence: 1 givenname: B. C. surname: Carlson fullname: Carlson, B. C. |
| BookMark | eNpt0MFKw0AQBuBFKthW8QU8BC-eojO7MZs91tJaoeKlgrew2Uw0Jd3U3Q3i25vaoiCehmE-Zph_xAa2tcTYOcI1opA3gCgBxREbIqjbWCJ_GbAhgEhjFEqdsJH3a-hVmqghe5xE09ZaMqFubXRH4YPIRrOGNmSDdp_RvLPfMx9pW0aL-vWNXLRy2npDttyh5tecsuNKN57ODnXMnuez1XQRL5_uH6aTZWw4iBBLMCBJQVZJpQrkCc-U1CVhqqHvMOEGTZFSIXmSiVKlBQnKqMoKw6UgEmN2ud-7de17Rz7k67Zztj-ZK8yAo0izHl3tkXGt946qfOvqTf9TjpDvosoPUfUy_iNNHfTuo-B03fzjL_Z-7UPrftZyUIonSnwBRJB0MQ |
| CitedBy_id | crossref_primary_10_1088_1402_4896_aceb1f crossref_primary_10_1016_0021_9045_92_90144_D crossref_primary_10_1216_rmjm_1030539686 crossref_primary_10_1137_0506084 crossref_primary_10_3390_fractalfract6060297 crossref_primary_10_1080_00029890_1971_11992791 crossref_primary_10_1137_0505060 crossref_primary_10_1016_0377_0427_94_00026_W crossref_primary_10_1137_0505076 crossref_primary_10_1137_0502040 crossref_primary_10_1137_1012078 crossref_primary_10_1137_0505026 crossref_primary_10_1137_0507023 crossref_primary_10_1137_0502032 crossref_primary_10_1137_0504035 crossref_primary_10_1016_0377_0427_94_90187_2 crossref_primary_10_1080_00029890_1975_11993837 crossref_primary_10_1016_S0022_247X_02_00354_2 crossref_primary_10_3390_e25111534 |
| Cites_doi | 10.1016/0022-247X(70)90276-3 10.1016/0022-247X(63)90067-2 10.1090/S0002-9939-1968-0222349-X 10.2307/1968644 10.1090/S0002-9939-1962-0140432-9 10.1090/S0025-5718-1966-0215497-8 |
| ContentType | Journal Article |
| Copyright | Copyright 1969 Society for Industrial and Applied Mathematics [Copyright] © 1969 © Society for Industrial and Applied Mathematics |
| Copyright_xml | – notice: Copyright 1969 Society for Industrial and Applied Mathematics – notice: [Copyright] © 1969 © Society for Industrial and Applied Mathematics |
| DBID | AAYXX CITATION 3V. 7RQ 7WY 7WZ 7X2 7XB 87Z 88A 88F 88I 88K 8AL 8FE 8FG 8FH 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI CCPQU D1I DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- KB. L.- L6V LK8 M0C M0K M0N M1Q M2O M2P M2T M7P M7S MBDVC P5Z P62 PATMY PDBOC PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS PYCSY Q9U U9A |
| DOI | 10.1137/0117013 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Career & Technical Education Database ProQuest ABI/INFORM Collection ABI/INFORM Global (PDF only) Agricultural Science Collection ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Biology Database (Alumni Edition) Military Database (Alumni Edition) Science Database (Alumni Edition) Telecommunications (Alumni Edition) Computing Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni Edition) Research Library (Alumni Edition) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection Agricultural & Environmental Science Collection ProQuest Central Essentials Biological Science Collection ProQuest Central ProQuest Business Premium Collection Technology Collection Natural Science Collection ProQuest One Community College ProQuest Materials Science Collection ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student Research Library Prep SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database Materials Science Database ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Biological Science Collection ABI/INFORM Global Agriculture Science Database Computing Database ProQuest Military Database (NC LIVE) ProQuest Research Library Science Database Telecommunications Database Biological Science Database Engineering Database Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Environmental Science Database Materials Science Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business (OCUL) ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection Environmental Science Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Agricultural Science Database ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest Military Collection ProQuest Central China ABI/INFORM Complete ProQuest Telecommunications ProQuest One Applied & Life Sciences Natural Science Collection Biological Science Collection ProQuest Central (New) Engineering Collection Career and Technical Education (Alumni Edition) Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Biological Science Collection ProQuest One Academic Eastern Edition Agricultural Science Collection ProQuest Technology Collection ProQuest Telecommunications (Alumni Edition) Biological Science Database ProQuest Business Collection Environmental Science Collection ProQuest Career and Technical Education ProQuest One Academic UKI Edition Environmental Science Database ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection ProQuest One Academic Middle East (New) Materials Science Collection ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Natural Science Collection ProQuest Biology Journals (Alumni Edition) ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Central Korea Agricultural & Environmental Science Collection Materials Science Database ProQuest Research Library ABI/INFORM Complete (Alumni Edition) ProQuest Materials Science Collection ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest Military Collection (Alumni Edition) ProQuest SciTech Collection Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
| DatabaseTitleList | Agricultural Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1095-712X |
| EndPage | 148 |
| ExternalDocumentID | 2571325771 10_1137_0117013 2099249 |
| GroupedDBID | -DZ -~X 123 2AX 4.4 7RQ 7WY 7X2 7XC 85S 88I 8CJ 8FE 8FG 8FH 8FL 8G5 AALVN AAWIL ABAWQ ABBHK ABFAN ABJCF ABPFR ABPPZ ABPQH ABUWG ABXSQ ABYWD ACBEA ACGFO ACGOD ACHJO ACIWK ACMTB ACNCT ACPRK ACTMH ACUBG ADBBV ADODI ADULT AENEX AEUPB AFKRA AFRAH AFVYC AFXHP AGLNM AIHAF ALMA_UNASSIGNED_HOLDINGS ALRMG ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI BPHCQ CCPQU CS3 CZ9 D1I D1J D1K DQDLB DSRWC DU5 DWQXO EBS ECEWR EJD ESX F5P FEDTE FRNLG FVMVE GNUQQ GUQSH HCIFZ HGD HQ6 HVGLF IPSME JAAYA JAS JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JST K6- K60 K6V K6~ K7- KB. KC. L6V LK5 LK8 M0C M0K M1Q M2O M2P M7P M7R M7S MVM NHB P1Q P2P P62 PATMY PDBOC PHGZM PHGZT PQBIZ PQBZA PQQKQ PROAC PTHSS PYCSY RJG RNS RSI SA0 T9H TN5 VOH WH7 YNT YXE YYP ~02 .4S .DC 8WZ A6W AAYJJ AAYXX ABDBF ABKAD ABMZU ABUFD ACUHS AFFHD ANXRF ARCSS CITATION DQ2 EAP EDO EMK EST H13 H~9 I-F PQGLB TAE TUS WHG XSW ZCG 3V. 7XB 88A 88K 8AL 8FK JQ2 L.- M0N M2T MBDVC PKEHL PQEST PQUKI PRINS Q9U U9A |
| ID | FETCH-LOGICAL-c203t-70c07e908f799b1242897ade16a0124142c1cb6eb72483d96be3e8ef8bc273ee3 |
| IEDL.DBID | M2P |
| ISICitedReferencesCount | 25 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=10_1137_0117013&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0036-1399 |
| IngestDate | Fri Jul 25 10:41:05 EDT 2025 Tue Nov 18 21:57:36 EST 2025 Sat Nov 29 03:53:09 EST 2025 Thu Jun 19 15:13:35 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c203t-70c07e908f799b1242897ade16a0124142c1cb6eb72483d96be3e8ef8bc273ee3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| PQID | 918021368 |
| PQPubID | 666314 |
| PageCount | 33 |
| ParticipantIDs | proquest_journals_918021368 crossref_primary_10_1137_0117013 crossref_citationtrail_10_1137_0117013 jstor_primary_2099249 |
| PublicationCentury | 1900 |
| PublicationDate | 19690101 1969-01-00 |
| PublicationDateYYYYMMDD | 1969-01-01 |
| PublicationDate_xml | – month: 1 year: 1969 text: 19690101 day: 1 |
| PublicationDecade | 1960 |
| PublicationPlace | Philadelphia |
| PublicationPlace_xml | – name: Philadelphia |
| PublicationTitle | SIAM journal on applied mathematics |
| PublicationYear | 1969 |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher_xml | – name: Society for Industrial and Applied Mathematics |
| References | Ahlfors Lars V. (R1) 1966 Jauch J. M. (R8) 1955 R4 Titchmarsh E. C. (R10) 1939 R5 R6 R9 Erdélyi Arthur (R7B) 1953 Carlson B. C. (R17) 1966; 8 R11 Erdélyi Arthur (R7A) 1953 R16 Bochner Salomon (R3) 1948 Feldheim Ervin (R13) 1943; 12 Whittaker E. T. (R12) 1927 Vilenkin N. Ja. (R15) 1964; 64 Apostol Tom M. (R2) 1957 Gindikin S. G. (R14) 1964; 19 |
| References_xml | – volume-title: Mathematical analysis: a modern approach to advanced calculus year: 1957 ident: R2 – volume: 8 start-page: 559 year: 1966 ident: R17 publication-title: SIAM Rev. – volume-title: Modern Analysis year: 1927 ident: R12 – ident: R5 doi: 10.1016/0022-247X(70)90276-3 – volume: 19 start-page: 3 year: 1964 ident: R14 publication-title: Uspehi Mat. Nauk – volume-title: Complex analysis: An introduction of the theory of analytic functions of one complex variable year: 1966 ident: R1 – volume-title: The Theory of Functions year: 1939 ident: R10 – volume: 12 start-page: 17 year: 1943 ident: R13 publication-title: Ann. Scuola Norm. Super. Pisa (2) – ident: R4 doi: 10.1016/0022-247X(63)90067-2 – volume: 64 start-page: 497 year: 1964 ident: R15 publication-title: Mat. Sb. (N.S.) – ident: R6 doi: 10.1090/S0002-9939-1968-0222349-X – volume-title: Higher transcendental functions. Vol. I year: 1953 ident: R7A – ident: R16 doi: 10.2307/1968644 – volume-title: Higher transcendental functions. Vol. II year: 1953 ident: R7B – ident: R11 doi: 10.1090/S0002-9939-1962-0140432-9 – volume-title: Several Complex Variables year: 1948 ident: R3 – volume-title: The theory of photons and electrons. The relativistic quantum field theory of charged particles with spin one-half year: 1955 ident: R8 – ident: R9 doi: 10.1090/S0025-5718-1966-0215497-8 |
| SSID | ssj0011649 |
| Score | 1.2135823 |
| Snippet | If f is holomorphic on a domain D in the complex plane, an analogous function F of several complex variables is constructed by taking a weighted average of f... If $\,f$ is holomorphic on a domain $D$ in the complex plane, an analogous function $F$ of several complex variables is constructed by taking a weighted... |
| SourceID | proquest crossref jstor |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 116 |
| SubjectTerms | Analytic functions Applied mathematics Entire functions Integers Integrals Integrands Line segments Mathematical functions Mathematical independent variables Partial differential equations Polynomials Rectifiable curves Series convergence Variables |
| Title | A Connection Between Elementary Functions and Higher Transcendental Functions |
| URI | https://www.jstor.org/stable/2099249 https://www.proquest.com/docview/918021368 |
| Volume | 17 |
| WOSCitedRecordID | wos10_1137_0117013&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: M0C dateStart: 19660101 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: P5Z dateStart: 19660101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Agriculture Science Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: M0K dateStart: 19660101 isFulltext: true titleUrlDefault: https://search.proquest.com/agriculturejournals providerName: ProQuest – providerCode: PRVPQU databaseName: Biological Science Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: M7P dateStart: 19530901 isFulltext: true titleUrlDefault: http://search.proquest.com/biologicalscijournals providerName: ProQuest – providerCode: PRVPQU databaseName: Career & Technical Education Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: 7RQ dateStart: 19660101 isFulltext: true titleUrlDefault: https://search.proquest.com/career providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: K7- dateStart: 19530901 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: M7S dateStart: 19530901 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: Environmental Science Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: PATMY dateStart: 19530901 isFulltext: true titleUrlDefault: http://search.proquest.com/environmentalscience providerName: ProQuest – providerCode: PRVPQU databaseName: Materials Science Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: KB. dateStart: 19530901 isFulltext: true titleUrlDefault: http://search.proquest.com/materialsscijournals providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest ABI/INFORM Collection customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: 7WY dateStart: 19660101 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: BENPR dateStart: 19660101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Military Database (NC LIVE) customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: M1Q dateStart: 19660101 isFulltext: true titleUrlDefault: https://search.proquest.com/military providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Research Library customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: M2O dateStart: 19660101 isFulltext: true titleUrlDefault: https://search.proquest.com/pqrl providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1095-712X dateEnd: 20140531 omitProxy: false ssIdentifier: ssj0011649 issn: 0036-1399 databaseCode: M2P dateStart: 19660101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB509aAH3-K6KjmIt2rT7DbNSVzZRZCu9YWPS2nTFARZdXcV_PfOpNmKCF68fDQkhdJJMjPJzHwA-2Hmi0xI48mwyDw0qQ0uKdnxCirtHfpChCK3ZBNyMIju71XiYnPGLqxyuifajbp40XRGfqSoVBkXYXT8-uYRaRRdrjoGjVmYQ8OGU0RXHCT1JQJ6AmpacxcNHVXlzHJOJX2IcIWLH8qoikf8tSdbRdNf_ucnrsCSszDZSTUlVmHGDNdgMa7Ls47XIT5hNsDF5jSwbhWqxXouknz0yfqo7eyEZNmwYFUsCLNqTVvKXLTYv8dswG2_d3N65jleBU8Hvph40te-NMqPSqlUjgoenS6ZFYaj4LDF24HmOg9NLoN2JAoV5kaYyJRRrtHYMUZsQmP4MjRblPHtG646pSjDDD1Rg8ZOGeFbUUncVu2iCQfTH5xqV3ScuC-eU-t8CJk6STSB1QNfqzobv4dsWAnV_ZT1i95jE1pTcaRuAY7TWhbbf_a2YIHqA1VnKjvQmIzezS7M64_J03i0B7Py6pLw7mEP5rq9QXKFrXPpEXYPEWP_1OI5IaexcXBhMbF4Qyjts7xGTDqPX0MZ3YE |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LS8NAEB5qFdSDz4q1Pvag3oJJts1mDyJVW1r6oIcKvcVkswFB0tpWpT_K_-js5iFS8NaDx7CbkGRm57E7830Al45vUp8yaTAn9A0MqSUuKVYzQgXt7ZiUOjTQZBOs33dHIz4owFfWC6PKKjObqA11OBZqj_yGK6gyizru3eTNUKRR6nA1Y9BItKIjF5-Ysc1u248o3ivbbjaGDy0jJRUwhG3SucFMYTLJTTdinAfo3TDjYH4oLXxrvLKqtrBE4MiA2VWXhtwJJJWujNxAoKeXkuJz12Adowjb1JWCg_zQAjMPnmH8YmDFkx5dy1IQQorgxaK_nF9S_7jkA7Rja-7-s1-yBztpBE3qicrvQ0HGB7Ddy-FnZ4fQqxNdwKN7Nsh9UopGGmml_HRBmujN9YIjfhySpNaFaLctNCUwZiQ_c0rwtJLvOYJiPI7lsepoN6XFaxGNHB8zbYnBXOTiXW6kuLuqYRmuM4F6IgVVV9wer55OrijzUsmXgeQTJwmOyPKUktaIfFx1NWN2XIZKJn4vNTAzL5f9yZ-jF7DZGva6Xrfd71RgS2EhJftHp1CcT9_lGWyIj_nLbHquVZnA86oV5RsTRSzU |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Connection+Between+Elementary+Functions+and+Higher+Transcendental+Functions&rft.jtitle=SIAM+journal+on+applied+mathematics&rft.au=Carlson%2C+B.+C&rft.date=1969-01-01&rft.pub=Society+for+Industrial+and+Applied+Mathematics&rft.issn=0036-1399&rft.eissn=1095-712X&rft.volume=17&rft.issue=1&rft.spage=116&rft_id=info:doi/10.1137%2F0117013&rft.externalDocID=2571325771 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0036-1399&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0036-1399&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0036-1399&client=summon |