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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
DOI: https://doi.org/10.1090/S0025-5718-1981-0628708-X
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: https://doi.org/10.1090/S0025-5718-1981-0628708-X
Keywords: Elliptic functions
Article copyright: © Copyright 1981 American Mathematical Society