On the Analytic Continuation of Lauricella–Saran Hypergeometric Function FK(a1,a2,b1,b2;a1,b2,c3;z)

The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions FK with some parameter values to the corresponding branched continued fractions in their domain of convergence. The PC method used here is based on the correspondence between a formal triple powe...

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Vydáno v:Mathematics (Basel) Ročník 11; číslo 21; s. 4487
Hlavní autoři: Antonova, Tamara, Dmytryshyn, Roman, Goran, Vitaliy
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.11.2023
Témata:
analytic continuation
branched continued fraction
convergence
holomorphic functions of several complex variables
Hypergeometric functions
Lauricella–Saran hypergeometric function
Neighborhoods
Polyvinylidene chlorides
Power series
ISSN:2227-7390, 2227-7390
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Shrnutí:The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions FK with some parameter values to the corresponding branched continued fractions in their domain of convergence. The PC method used here is based on the correspondence between a formal triple power series and a branched continued fraction. As additional results, analytical extensions of the Lauricella–Saran hypergeometric functions FK(a1,a2,1,b2;a1,b2,c3;z) and FK(a1,1,b1,b2;a1,b2,c3;z) to the corresponding branched continued fractions were obtained. To illustrate this, we provide some numerical experiments at the end.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11214487