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Date: 18-9-2019
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Date: 17-9-2018
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Date: 20-8-2018
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The functions
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where and are the Jacobi theta functions and is the complete elliptic integral of the first kind.
The Neville theta functions are implemented in the Wolfram Language as NevilleThetaC[z, m], NevilleThetaD[z, m], NevilleThetaN[z, m], and NevilleThetaS[z, m].
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). "Neville's Notation for Theta Functions." §16.36 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 578-579, 1972.
Neville, E. H. Jacobi Elliptic Functions, 2nd ed. London: Oxford University Press, 1951.
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