Error functions, Mordell integrals and an integral analogue of a partial theta function
DOI10.4064/aa8207-5-2016zbMath1393.11058arXiv1605.08904OpenAlexW2963744698MaRDI QIDQ2957226
Alexandru Zaharescu, Atul Dixit, Arindam Roy
Publication date: 25 January 2017
Published in: Acta Arithmetica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1605.08904
Riemann zeta functionhypergeometric functionsasymptotic expansionsDirichlet \(L\)-functionpartial theta functionRamanujan's lost notebookMordell integrals
(zeta (s)) and (L(s, chi)) (11M06) Asymptotic expansions of solutions to ordinary differential equations (34E05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)
Related Items (3)
Uses Software
Cites Work
- Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
- Character analogues of theorems of Ramanujan, Koshliakov and Guinand
- A nearly-optimal method to compute the truncated theta function, its derivatives, and integrals
- Fast methods to compute the Riemann zeta function
- The Mordell integral, quantum modular forms, and mock Jacobi forms
- Riesz-type criteria and theta transformation analogues
- Ramanujan's ``lost notebook. I: Partial Theta-functions
- Some elegant approximations and asymptotic formulas of Ramanujan
- Analogues of the general theta transformation formula
- An Integral Analogue of Theta Functions and Gauss Sums in Ramanujan's Lost Notebook
- Computing the truncated theta function via Mordell integral
- Ramanujan's Lost Notebook
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