More infinite products: Thue–Morse and the gamma function
Letting ( t n ) denote the Thue–Morse sequence with values 0, 1, we note that the Woods–Robbins product ∏ n ≥ 0 2 n + 1 2 n + 2 ( - 1 ) t n = 2 - 1 / 2 involves a rational function in n and the ± 1 Thue–Morse sequence ( ( - 1 ) t n ) n ≥ 0 . The purpose of this paper is twofold. On the one hand, we...
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| Vydáno v: | The Ramanujan journal Ročník 49; číslo 1; s. 115 - 128 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.05.2019
Springer Nature B.V Springer Verlag |
| Témata: | |
| ISSN: | 1382-4090, 1572-9303 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Letting
(
t
n
)
denote the Thue–Morse sequence with values 0, 1, we note that the Woods–Robbins product
∏
n
≥
0
2
n
+
1
2
n
+
2
(
-
1
)
t
n
=
2
-
1
/
2
involves a rational function in
n
and the ± 1 Thue–Morse sequence
(
(
-
1
)
t
n
)
n
≥
0
. The purpose of this paper is twofold. On the one hand, we try to find other rational functions for which similar infinite products involving the ± 1 Thue–Morse sequence have an expression in terms of known constants. On the other hand, we also try to find (possibly different) rational functions
R
for which the infinite product
∏
R
(
n
)
t
n
also has an expression in terms of known constants. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1382-4090 1572-9303 |
| DOI: | 10.1007/s11139-017-9981-7 |