Neville theta functions
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In mathematics, the Neville theta functions, named after Eric Harold Neville,[1] are defined as follows:[2][3] [4]
where:
- is the elliptic nome
Examples
Substitute z = 2.5, m = 0.3 into the above definitions of Neville theta functions(using Maple) once obtain the following(consistent with results from wolfram math).
Symmetry
Complex 3D plots
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Implementation
NetvilleThetaC[z,m], NevilleThetaD[z,m], NevilleThetaN[z,m], and NevilleThetaS[z,m] are built-in functions of Mathematica[6] No such functions in Maple.
Notes
- ^ Abramowitz and Stegun, pp. 578-579
- ^ Neville (1944)
- ^ wolfram Mathematic
- ^ wolfram math
- ^ [1]
- ^ [2]
References
- Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.
- Neville, E. H. (Eric Harold) (1944). Jacobian Elliptic Functions. Oxford Clarendon Press.
- Weisstein, Eric W. "Neville Theta Functions". MathWorld.