A symbolic decision procedure for relations arising among Taylor coefficients of classical Jacobi theta functions. (September 2017)

• Record Type: Journal Article
• Authors: Ye, Liangjie
• Is Part Of: Journal of symbolic computation. Volume 82(2017)
• Page Start: 134
• Page End: 163
• Publication Date: 2017-09
• Subjects: Jacobi theta functions -- Modular forms -- Algorithmic zero-recognition -- Computer algebra -- Automatic proving of special function identities; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.01.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The class of objects we consider are algebraic relations between the four kinds of classical Jacobi theta functions θ j ( z | τ ), j = 1, …, 4, and their derivatives. We present an algorithm to prove such relations automatically where the function argument z is zero, but where the parameter τ in the upper half complex plane is arbitrary.