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), 851-855

MSC:
Primary 33A25

DOI:
https://doi.org/10.1090/S0025-5718-1975-0367322-8

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 with integer coefficients, . 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 . A table of the first 59 of these integers is given. The table is of number-theoretical interest as well as useful for calculating complete and incomplete elliptic integrals.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0367322-8

Keywords:
Elliptic integrals,
theta functions,
nome,
partitions,
reversion

Article copyright:
© Copyright 1975
American Mathematical Society