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Calculation of coefficients in a power-series expansion of the nome q = exp[-π K(k')K(k)]

✍ Scribed by D.K. Lee

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
321 KB
Volume
70
Category
Article
ISSN
0010-4655

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✦ Synopsis

A recurrence relation is derived for expansion coefficients in a power series of the nome q exp[-rrK(k')/K(k)]= + ~, where K(k) is the complete elliptic integral of the first kind, k' = (1-k 2)'~2, and A = ~(1 -k '~2/(i + k~I~~2)• A simple numerical method based on the recurrence relation is developed for calculation of the coefficients a,,,. Analysis of errors arising from truncation of the power series for q suggests that numerical evaluation of q from this series is more useful than other known methods, except when k is very close to unity.

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