Results 21 to 30 of about 639 (70)

Sufficiency for Gaussian hypergeometric functions to be uniformly convex

International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 4, Page 765-773, 1999., 1999
Let F(a, b; c; z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z) = zF(a, b; c; z)*f(z). In this paper the authors identify two subfamilies of analytic functions ℱ1 and ℱ2 and obtain conditions on the parameters a, b, c such that f ∈ ℱ1 ...
Yong Chan Kim, S. Ponnusamy
wiley   +1 more source

Generalized fractional calculus to a subclass of analytic functions for operators on Hilbert space

International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 4, Page 671-676, 1998., 1996
In this paper, we investigate some generalized results of applications of fractional integral and derivative operators to a subclass of analytic functions for operators on Hilbert space.
Yong Chan Kim, Jae Ho Choi, Jin Seop Lee
wiley   +1 more source

Generalized Bessel function of Type D [PDF]

, 2008
We write down the generalized Bessel function associated with the root system of type $D$ by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type $D$.Comment: This is a ...
Demni, Nizar
core   +6 more sources

Transformation formulas for terminating Saalschützian hypergeometric series of unit argument

International Journal of Stochastic Analysis, Volume 8, Issue 2, Page 189-194, 1995., 1994
Transformation formulas for terminating Saalschützian hypergeometric series of unit argument p+1Fp(1) are presented. They generalize the Saalschützian summation formula for 3F2(1). Formulas for p = 3, 4, 5 are obtained explicitly, and a recurrence relation is proved by means of which the corresponding formulas can also be derived for larger p.
Wolfgang Bühring
wiley   +1 more source

Generalized Neumann and Kapteyn expansions

International Journal of Stochastic Analysis, Volume 8, Issue 4, Page 415-421, 1995., 1995
Certain formal series of a most general nature are specialized so as to deduce expansions in terms of a class of generalized hypergeometric functions. These series generalize the Neumann and Kapteyn series in the theory of Bessel functions, and their convergence is investigated. An example of a succinct expansion is also given.
Harold Exton
wiley   +1 more source

Some extensions of Bateman′s product formulas for the Jacobi polynomials

International Journal of Stochastic Analysis, Volume 8, Issue 4, Page 423-428, 1995., 1995
The authors derive generalizations of some remarkable product formulas of Harry Bateman (1882‐1946) for the classical Jacobi polynomials. They also show how the results considered here would lead to various families of linear, bilinear, and bilateral generating functions for the Jacobi and related polynomials.
Ming-Po Chen, H. M. Srivastava
wiley   +1 more source

A Particular Solution of a Painlev\'e System in Terms of the Hypergeometric Function ${}_{n+1}F_n$ [PDF]

, 2010
In a recent work, we proposed the coupled Painlev\'e VI system with $A^{(1)}_{2n+1}$-symmetry, which is a higher order generalization of the sixth Painlev\'e equation ($P_{\rm VI}$).
Suzuki, Takao
core   +5 more sources

Generalized Fractional Integral Operators Involving the H―-Function and Their Applications to Special Functions

Abstract and Applied Analysis
MSC2020 Classification: 26A33, 33B15, 33C05, 33C20, 44A10, 44A20.
S. Chandak, B. K. Tripathi, Biniyam Shimelis   +2 more
doaj   +1 more source

A p-adic analogue of a formula of Ramanujan [PDF]

, 2007
During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured $p$-adic analogues to such formulae. Using a combination of ordinary and
McCarthy, Dermot, Osburn, Robert
core   +4 more sources

On the Generalized Class of Multivariable Humbert‐Type Polynomials

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The present paper deals with the class of multivariable Humbert polynomials having generalization of some well‐known polynomials like Gegenbauer, Legendre, Chebyshev, Gould, Sinha, Milovanović‐Djordjević, Horadam, Horadam‐Pethe, Pathan and Khan, a class of generalized Humbert polynomials in two variables etc.
B. B. Jaimini, Meenu, S. D. Purohit, D. L. Suthar, Shikha Binwal   +4 more
wiley   +1 more source