Jacobi Theta Functions
The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are quasi-doubly periodic, and are most commonly denoted ϑ_n(z, q) in modern texts, although the notations Θ_n(z, q) and θ_n(z, q) are sometimes also used. Whittaker and Watson gives a table summarizing notations used by various earlier writers. The theta functions are given in the Wolfram Language by EllipticTheta[n, z, q], and their derivatives are given by EllipticThetaPrime[n, z, q]. The translational partition function for an ideal gas can be derived using elliptic theta functions.
Blecksmith-Brillhart-Gerst theorem | Dedekind eta function | elliptic function | half-period ratio | Jacobi elliptic functions | Jacobi's imaginary transformation | Jacobi triple product | Landen's formula | mock theta function | modular equation | Mordell integral | Neville theta functions | nome | pentagonal number theorem | Poincaré-Fuchs-Klein automorphic function | quintuple product identity | Ramanujan theta functions | Schröter's formula | sum of squares function | Weber functions
Carl Jacobi