HYPERGEOMETRIC

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Asymptotic Approximation of the Eigenvalues and the Eigenfunctions for the Orr-Sommerfeld Equation on Infinite Intervals
《Advances in Pure Mathematics》2019年第12期967-989,共23页Victor Nijimbere 
Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurati...
关键词：EIGENVALUES EIGENFUNCTIONS Infinite Intervals WKB Methods Long-Wave LIMIT APPROXIMATION Short-Wave LIMIT APPROXIMATION Generalized HYPERGEOMETRIC Functions 
Chebyshev Polynomials with Applications to Two-Dimensional Operators被引量：1
《Advances in Pure Mathematics》2019年第12期990-1033,共44页Alfred Wünsche 
A new application of Chebyshev polynomials of second kind Un(x) to functions of two-dimensional operators is derived and discussed. It is related to the Hamilton-Cayley identity for operators or matrices which allows ...
关键词：HYPERGEOMETRIC Function JACOBI POLYNOMIALS Ultraspherical POLYNOMIALS Chebyshev POLYNOMIALS LEGENDRE POLYNOMIALS Hamilton-Cayley Identity Generating Functions FIBONACCI and Lucas Numbers Special LORENTZ Transformations Coordinate-Invariant Methods 
Generalized Eulerian Numbers
《Advances in Pure Mathematics》2018年第3期335-361,共27页Alfred Wünsche 
We generalize the Eulerian numbers ?to sets of numbers Eμ(k,l), (μ=0,1,2,···) where the Eulerian numbers appear as the special case μ=1. This can be used for the evaluation of generalizations Eμ(k,Z) of the Geo...
关键词：EULERIAN NUMBERS EULERIAN Polynomials STIRLING NUMBERS PERMUTATIONS Binomials HYPERGEOMETRIC Functions Geometric Series Vandermonde’s Convolution Identity Recurrence Relations Operator ORDERINGS 
Kummer’s 24 Solutions of the Hypergeometric Differential Equation with the Aid of Fractional Calculus
《Advances in Pure Mathematics》2016年第3期180-191,共12页Tohru Morita Ken-ichi Sato 
We know that the hypergeometric function, which is a solution of the hypergeometric differential equation, is expressed in terms of the Riemann-Liouville fractional derivative (fD). The solution of the differential eq...
关键词：Fractional Derivative Hypergeometric Differential Equation Hypergeometric Function 
Wright Type Hypergeometric Function and Its Properties
《Advances in Pure Mathematics》2013年第3期335-342,共8页Snehal B. Rao Jyotindra C. Prajapati Ajay K. Shukla 
Let s and z be complex variables, Γ(s) be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as: where which is a di...
关键词：Euler TRANSFORM Fox H-FUNCTION WRIGHT TYPE HYPERGEOMETRIC FUNCTION Laplace TRANSFORM Mellin TRANSFORM Whittaker TRANSFORM WRIGHT HYPERGEOMETRIC FUNCTION 
Applications of Multivalent Functions Associated with Generalized Fractional Integral Operator
《Advances in Pure Mathematics》2013年第1期1-5,共5页Jae Ho Choi 
By using a method based upon the Briot-Bouquet differential subordination, we investigate some subordination properties of the generalized fractional integral operator which was defined by Owa, Saigo and Srivastava [1...
关键词：MULTIVALENT Functions SUBORDINATION GAUSSIAN HYPERGEOMETRIC Function FRACTIONAL INTEGRAL Operator 
On Humbert Matrix Polynomials of Two Variables
《Advances in Pure Mathematics》2012年第6期423-427,共5页Ghazi S. Khammash A. Shehata 
In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansi...
关键词：HUMBERT MATRIX POLYNOMIALS of TWO VARIABLES HYPERGEOMETRIC MATRIX Function MATRIX Functional Calculus 
A New Extension of Humbert Matrix Function and Their Properties
《Advances in Pure Mathematics》2011年第6期315-321,共7页Mohamed Abul-Dahab Ayman Shehata 
This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix functio...
关键词：HYPERGEOMETRIC MATRIX FUNCTION HUMBERT MATRIX FUNCTION Kummer MATRIX FUNCTION INTEGRAL REPRESENTATIONS 
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