A modular-type formula for \((x;q)_\infty \)
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Publication:1635637
DOI10.1007/s11139-017-9967-5zbMath1441.11089OpenAlexW2774933984MaRDI QIDQ1635637
Publication date: 31 May 2018
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-017-9967-5
\(q\)-seriesLambert seriesDedekind \(\eta \)-functionJacobi \(\theta \)-functionmodular elliptic functions
(q)-calculus and related topics (05A30) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Theta series; Weil representation; theta correspondences (11F27) Dedekind eta function, Dedekind sums (11F20) Elliptic functions and integrals (33E05)
Related Items
On theta-type functions in the form \((x; q)_\infty\), Analytical study of the pantograph equation using Jacobi theta functions
Cites Work
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- On the modular behaviour of the infinite product \((1-x)(1-xq)(1-xq^2)(1-xq^3)\dots\)
- Problèmes de modules pour des équations différentielles non linéaires du premier ordre
- Zeros of entire functions and a problem of Ramanujan
- On summability of formal solutions to a Cauchy problem and generalization of Mordell's theorem
- Elementary proof of the transformation formula for Lambert series involving generalized Dedekind sums
- Multiple gamma functions and multiple \(q\)-gamma functions
- Développements asymptotiques \(q\)-Gevrey et séries \(Gq\)-sommables. (\(q\)-Gevrey asymptotic expansions and \(Gq\)-summable series.)
- Some asymptotic formulae for \(q\)-shifted factorials
- About Jackson \(q\)-Bessel functions
- On Poisson's summation formula
- Generalized Dedekind sums and transformation formulae of certain Lambert series
- Galois theory of fuchsian q-difference equations
- Séries divergentes et développements asymptotiques
- Local analytic classification of q-difference equations
- A simple proof of η(— 1/τ)= η(τ)√τ/i
- FUNCTIONAL EQUATIONS AND SELF-RECIPROCAL FUNCTIONS CONNECTED WITH LAMBERT SERIES