Results 1 to 10 of about 418 (20)
The roots of the third Jackson q‐Bessel function
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 67, Page 4241-4248, 2003., 2003 We derive analytic bounds for the zeros of the third Jackson q‐Bessel function Jv(3)(z;q).
L. D. Abreu, J. Bustoz, J. L. Cardoso
wiley +1 more source
A Connection Formula of the Hahn-Exton $q$-Bessel Function [PDF]
, 2011 We show a connection formula of the Hahn-Exton $q$-Bessel function around the origin and the infinity. We introduce the $q$-Borel transformation and the $q$-Laplace transformation following C. Zhang to obtain the connection formula. We consider the limit
Morita, Takeshi
core +4 more sources
q-hypergeometric double sums as mock theta functions [PDF]
, 2012 Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums ...
Andrews +5 more
core +3 more sources
Duality for Finite Multiple Harmonic q-Series [PDF]
, 2004 We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial coefficients ...
Andrews +24 more
core +2 more sources
On two 10th order mock theta identities
, 2013 We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan ...
A. Folsom +8 more
core +3 more sources
, 2010 The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients.
Warnaar, S. Ole, Zudilin, Wadim
core +1 more source
The q-WZ Method for Infinite Series [PDF]
, 2008 Motivated by the telescoping proofs of two identities of Andrews and Warnaar, we find that infinite q-shifted factorials can be incorporated into the implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and Mu to prove nonterminating
Chen, William Y. C., Xia, Ernest X. W.
core +2 more sources
Ramanujan-type formulae for $1/\pi$: $q$-analogues
, 2018 The hypergeometric formulae designed by Ramanujan more than a century ago for efficient approximation of $\pi$, Archimedes' constant, remain an attractive object of arithmetic study.
Guo, Victor J. W., Zudilin, Wadim
core +2 more sources
An elementary proof of the irrationality of Tschakaloff series
, 2005 We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.Comment:
A. Poorten van der +10 more
core +2 more sources
On three theorems of Folsom, Ono and Rhoades
, 2013 In his deathbed letter to Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom,
Zudilin, Wadim
core +1 more source