Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function 𝑠𝑛(𝑥,𝑘)

Fransén, Arne

doi:10.1090/S0025-5718-1981-0628708-X

Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function $\textrm {sn}(x, k)$
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Math. Comp. 37 (1981), 475-494 Request permission

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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