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Certain Families of Elliptic Functions Defined by <Emphasis Type="Italic">q</Emphasis>-Series |
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| Authors: | |
| Institution: | (1) Department of Mathematics, Tokyo Institute of Technology, Meguro Tokyo, 152-0033, Japan;(2) Faculty of Mathematics, Kyushu University, Hakozaki Fukuoka, 812-8581, Japan |
| Abstract: | We introduce certain families of elliptic functions involving the Weierstrass ℘-function via q-series systematically and investigate their analytic and algebraic properties. Especially, we give examples of non-linear algebraic ordinary differential equations satisfied by some such elliptic functions. 2000 Mathematics Subject Classification: Primary–11M36, 33E05 |
| Keywords: | q-series Weierstrass ℘ -function elliptic functions Eisenstein series algebraic differential equations q-gamma function |
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