Finite Rogers-Ramanujan type identities.
Fuchsian differential equation for the perimeter generating function of three-choice polygons.
Generalization of two identities in Ramanujan's lost notebook
Hankel Transform in Quantum Calculus and Applications
Mathematics Subject Classification: 44A15, 33D15, 81Q99This paper is devoted to study the q-Hankel transform associated with the third q-Bessel function called also Hahn-Exton function. We use the q- approximation of unit for establishing a q-inverse formula of this transform. Moreover, we establish the related q-Parseval theorem.
Heine's basic transform and a permutation group for q-harmonic series
Heisenberg uncertainty principles for some -analogue Fourier transforms.
Hurwitz and Tasoev continued fractions with long period.
HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Hypergeometric -functions of the -Painlevé system of type .
Hypergeometric functions of the -Painlevé systems of type .
In praise of an elementary identity of Euler.
Integral identities and constructions of approximations to zeta-values
Some general construction of linear forms with rational coefficients in values of Riemann zeta-function at integer points is presented. These linear forms are expressed in terms of complex integrals of Barnes type that allows to estimate them. Some identity connecting these integrals and multiple integrals on the real unit cube is proved.
Interpolation of entire functions on regular sparse sets and -Taylor series
We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.
Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets
Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60This paper aims to study the q-wavelets and the continuous q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. Using the q-Riemann-Liouville and the q-Weyl transforms, we give some relations between the continuous q-wavelet transform, studied in [3], and the continuous q-wavelet transform associated with the q-Bessel operator, and we deduce formulas which give the inverse operators of the q-Riemann-Liouville and...
Inversion of bilateral basic hypergeometric series.
Multivariate -adic fermionic -integral on and related multiple zeta-type functions.
New identities for the Rogers-Ramanujan functions
Noncommutative extensions of Ramanujan's summation.
Note on -extensions of Euler numbers and polynomials of higher order.
Note on the -extension of Barnes' type multiple Euler polynomials.