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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function $ {\rm sn}(x,\,k)$


Author: Arne FransΓ©n
Journal: Math. Comp. 37 (1981), 475-494
MSC: Primary 33A25
MathSciNet review: 628708
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Abstract: Two conjectures are posed for the coefficients introduced by Alois Schett in the Taylor series expansion of the Jacobian elliptic function $ {\text{sn}}(x,k)$. The first conjecture is furnished with a proof revealing a procedure which might be useful when calculating further coefficients. Some of the coefficients are tabulated.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0628708-X
PII: S 0025-5718(1981)0628708-X
Keywords: Elliptic functions
Article copyright: © Copyright 1981 American Mathematical Society