A partition formula for the integer coefficients of the theta function nome
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- by Helaman Rolfe Pratt Ferguson, Dale E. Nielsen and Grant Cook PDF
- Math. Comp. 29 (1975), 851-855 Request permission
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 number-theoretical interest as well as useful for calculating complete and incomplete elliptic integrals.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 851-855
- MSC: Primary 33A25
- DOI: https://doi.org/10.1090/S0025-5718-1975-0367322-8
- MathSciNet review: 0367322