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Factorial study of a certain parametric distribution.

A. Y. Yehia, K. I. Hamouda, Assem A. Tharwat (1991)

Trabajos de Estadística

The general theory of factorial analysis of continuous correspondance (FACC) is used to investigate the binary case of a continuous probability measure defined as:T(x,y) = ayn + b, (x,y) ∈ D & n ∈ N = 0, elsewhereWhere n ≥ 0, a and b are the parameters of this distribution, while the domain D is a variable trapezoidal inscribed in the unit square. The trapezoid depends on two parameters α and β.This problem is solved. As special cases of our problem we obtain a complete solution for...

Factorization of the hypergeometric-type difference equation on the uniform lattice.

Álvarez-Nodarse, R., Atakishiyev, N.M., Costas-Santos, R.S. (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Finite and infinite series involving MacRobert's E-Function

Ragab, Shahwar F. (1993)

Portugaliae mathematica

Finite monodromy of Pochhammer equation

Yoshishige Haraoka (1994)

Annales de l'institut Fourier

We consider the monodromy group $G$ of the Pochhammer differential equation $𝒫$ . Let $𝒫_{p}$ be the reduce equation modulo a prime $p$ . Then we show that $G$ is finite if and only if $𝒫_{p}$ has a full set of polynomial solutions for almost all primes $p$ .

First hitting time of the boundary of the Weyl chamber by radial Dunkl processes.

Demni, Nizar (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc

Zouhaïr Mouayn (2007)

Applications of Mathematics

We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions $Ψ_{μ, α}$ on a concrete realization of the universal covering group of $U (1, 1)$ . We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to $μ$ , and corresponding to the eigenvalue $4 α (α - 1)$ .

Fonctions généralisées sphériques sur $G_{ℂ} / G_{ℝ}$

Pascale Harinck (1990)

Annales scientifiques de l'École Normale Supérieure

Fonctions hypergéométriques en plusieurs variables et espaces des modules de variétés abéliennes

Paula Beazley Cohen, Jürgen Wolfart (1993)

Annales scientifiques de l'École Normale Supérieure

Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique

Jacques Faraut (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A Gutzmer formula for the complexification of a Riemann symmetric space. We consider a complex manifold $Ω$ and a real Lie group $G$ of holomorphic automorphisms of $Ω$ . The question we study is, for a holomorphic function $f$ on $Ω$ , to evaluate the integral of ${|f|}^{2}$ over a $G$ -orbit by using the harmonic analysis of $G$ . When $Ω$ is an annulus in the complex plane and $G$ the rotation group, it is solved by a classical formula which is sometimes called Gutzmer’s formula. We establish a generalization of it when $Ω$ is...

Fourier transform of $h_{n} (x + p) h_{n} (x - p)$ .

Ismail, Mourad E.H., Stempak, Krzystztof (1997)

International Journal of Mathematics and Mathematical Sciences

Four-term recurrence relations for hypergeometric functions of the second order. II.

Harold Exton (1998)

Collectanea Mathematica

The recent work on four-term recurrence relations for the second order functions of hypergeometric type undertaken by the author is developed from a slightly different point of view also using generating functions. The direction of future prospects is indicated.

Four-term recurrence relations for hypergeometric functions of the second order. I.

Harold Exton (1996)

Collectanea Mathematica

Four-term recurrence relations for hypergeometric functions of the second order are deduced from generating functions involving elementary functions. Generalisations are indicated and an example is given of a five-term recurrence for the confluent hypergeometric function.

Fractional Calculus of P-transforms

Kumar, Dilip, Kilbas, Anatoly (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform in reaction rate...

Fractional Calculus of the Generalized Wright Function

Kilbas, Anatoly (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 33C20.The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered.* The present investigation was partially supported...

Fractional derivative of the multivariable polynomials.

Chaurasia, V.B.L., Singhal, Vijay Kumar (2004)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

Gogovcheva, Elena, Boyadjiev, Lyubomir (2005)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 26A33, 33C45This paper refers to a fractional order generalization of the classical Jacobi polynomials. Rodrigues’ type representation formula of fractional order is considered. By means of the Riemann–Liouville operator of fractional calculus fractional Jacobi functions are defined, some of their properties are given and compared with the corresponding properties of the classical Jacobi polynomials. These functions appear as a special case of a fractional Gauss...

Fractional Integration and Fractional Differentiation of the M-Series

Sharma, Manoj (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 33C60, 44A15In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note that the Mittag-Leffler ...

Fractional Integration of the Product of Bessel Functions of the First Kind

Kilbas, Anatoly, Sebastian, Nicy (2010)

Fractional Calculus and Applied Analysis

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine...

From double Hecke algebra to analysis.

Cherednik, Ivan (1998)

Documenta Mathematica

Functional Analysis, Orthogonal Polynomials And A Theorem Of Markov.

Jairo A. Charris, Luis A. Gomez (1988)

Revista colombiana de matematicas

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