Results 51 to 60 of about 744 (75)

On the Generalized Associated Legendre Functions [PDF]

, 2008
Mathematics Subject Classification: 33C60, 33C20, 44A15This paper is devoted to an important case of Wright’s hypergeometric function 2Fτ,β1(a, b; c; z) = 2Fτ,β1(z), to studying its basic properties and to application of 2Fτ,β1(z) to the generalization ...
Rumiantseva, Olena, Virchenko, Nina
core  

A generating function of the squares of Legendre polynomials

, 2012
We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we
Zudilin, Wadim
core   +1 more source

Solutions of certain initial-boundary value problems via a new extended Laplace transform

Nonlinear Engineering
In this article, we present a novel extended exponential kernel Laplace-type integral transform. The Laplace, natural, and Sumudu transforms are all included in the suggested transform.
Almalki Yahya, Akel Mohamed, Abdalla Mohamed   +2 more
doaj   +1 more source

Sums of quadratic half integer harmonic numbers of alternating type

, 2016
Half integer values of quadratic harmonic numbers and reciprocal binomial coefficients sums are investigated in this paper. Closed form representations of double integral expressions are developed in terms of special functions.
A. Sofo
semanticscholar   +1 more source

\pi and other formulae implied by hypergeometric summation theorems [PDF]

, 2012
By employing certain extended classical summation theorems, several surprising \pi and other formulae are ...
Kim, Yong Sup, Rathie, Arjun K., Wang, Xiaoxia   +2 more
core  

Binomial sums related to rational approximations to $\zeta(4)$

, 2003
For the solution $\{u_n\}_{n=0}^\infty$ to the polynomial recursion $(n+1)^5u_{n+1}-3(2n+1)(3n^2+3n+1)(15n^2+15n+4)u_n -3n^3(3n-1)(3n+1)u_{n-1}=0$, where $n=1,2,...$, with the initial data $u_0=1$, $u_1=12$, we prove that all $u_n$ are integers.
Zudilin, Wadim
core   +1 more source

"Divergent" Ramanujan-type supercongruences

, 2010
"Divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases.
Guillera, Jesús, Zudilin, Wadim
core   +2 more sources

On Hankel Transform of Generalized Mathieu Series [PDF]

, 2009
Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20By using integral representations for several Mathieu type series, a number of integral transforms of Hankel type are derived here for general families of Mathieu ...
Tomovski, Živorad
core  

On the Laplace transform of absolutely monotonic functions

, 2016
We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function.
Koumandos, Stamatis, Pedersen, Henrik L.
core   +1 more source

Quantum alpha-determinants and q-deformed hypergeometric polynomials

, 2009
The quantum $\alpha$-determinant is defined as a parametric deformation of the quantum determinant. We investigate the cyclic $\mathcal{U}_q(\mathfrak{sl}_2)$-submodules of the quantum matrix algebra $\mathcal{A}_q(\mathrm{Mat}_2)$ generated by the ...
Kimoto, Kazufumi
core   +2 more sources