A partition formula for the integer coefficients of the theta function nome
Authors:
Helaman Rolfe Pratt Ferguson, Dale E. Nielsen and Grant Cook
Journal:
Math. Comp. 29 (1975), 851855
MSC:
Primary 33A25
DOI:
https://doi.org/10.1090/S00255718197503673228
MathSciNet review:
0367322
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Abstract  References  Similar Articles  Additional Information
Abstract: In elliptic function theory, the nome q can be given as a power series in $\varepsilon$ with integer coefficients, $q = {\Sigma _{n \geqslant 0}}{\delta _n}{\varepsilon ^{4n + 1}}$. Heretofore, the first 14 coefficients were calculated with considerable difficulty. In this paper, an explicit and general formula involving partitions is given for all the ${\delta _n}$. A table of the first 59 of these integers is given. The table is of numbertheoretical interest as well as useful for calculating complete and incomplete elliptic integrals.

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Additional Information
Keywords:
Elliptic integrals,
theta functions,
nome,
partitions,
reversion
Article copyright:
© Copyright 1975
American Mathematical Society