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On the Expansions of the Elliptic and Zeta Functions of 2/3K in Powers of q

โœ Scribed by Glaisher, J. W. L.


Book ID
120104414
Publisher
Oxford University Press
Year
1905
Tongue
English
Weight
279 KB
Volume
s2-2
Category
Article
ISSN
0024-6115

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๐Ÿ“œ SIMILAR VOLUMES


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*Zeta and q-Zeta Functions and Associated Series and Integrals* is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory

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A recurrence relation is derived for expansion coefficients in a power series of the nome q exp[-rrK(k')/K(k)]= + ~, where K(k) is the complete elliptic integral of the first kind, k' = (1-k 2)'~2, and A = ~(1 -k '~2/(i + k~I~~2)โ€ข A simple numerical method based on the recurrence relation is develop