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On some properties of the bibasic Humbert hypergeometric functions Ξ1 and Ξ2
The main object of this paper is to deduce the bibasic Humbert functions Ξ 1 and Ξ 2 Some interesting results and elementary summations technique that...
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On (p, q)-Appell Polynomials
We introduce polynomial sets of ( p , q )-Appell type and give some characterizations of them. The algebraic properties of the set of all polynomial...
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On σ-type zero of Sheffer polynomials
The main object of this paper is to investigate some properties of σ -type polynomials in one and two variables.
MSC: 33C65, 33E99, 44A45, 46G25.
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Some properties of the generalized Apostol-type polynomials
In this paper, we study some properties of the generalized Apostol-type polynomials (see (Luo and Srivastava in Appl. Math. Comput. 217:5702-5728,...
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Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations
The main object of this paper is to investigate several general families of hyper-geometric polynomials and their associated multiple integral...
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The Second Appell Function for one Large Variable
We consider the Mellin convolution integral representation of the second Appell function given in [8]. Then, we apply the asymptotic method designed...
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A generalization of Clausen’s identity
The paper gives an extension of Clausen’s identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related...
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On the Exponential Transform of Lemniscates
It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In...
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Recursive Three-Term Recurrence Relations for the Jacobi Polynomials on a Triangle
Given a suitable weight on ℝ d , there exist many (recursive) three-term recurrence relations for the corresponding multivariate orthogonal...
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An Explicit Formula for the Coefficients of the Saddle Point Method
Most standard textbooks about asymptotic approximations of integrals do not give explicit formulas for the coefficients of the asymptotic methods of...
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A two-parameter generalization of the complete elliptic integral of second kind
A two-parameter generalization of the complete elliptic integral of second kind is expressed in terms of the Appell function F ...
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On certain generalized families of unified elliptic-type integrals pertaining to Euler integrals and generating functions
Elliptic-type integrals have their importance and potential in certain problems in radiation physics and nuclear technology. A number of earlier...
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Uniformization by Lauricella Functions — An Overview of the Theory of Deligne-Mostow
This is a survey of the Deligne-Mostow theory of Lauricella functions, or what almost amounts to the same, of the period map for cyclic coverings of...
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Some Closed-Form Evaluations of Multiple Hypergeometric and q-Hypergeometric Series
The main object of the present paper is to show how some fairly general analytical tools and techniques can be applied with a view to deriving...
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Eigenfunctions of Two-Scale Difference Equations with Rational Symbol
This paper deals with two-scale difference equations having a formal power series as symbol. We require that the equation has non-zero distributional...
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On Properties of the Legendre Differential Expression
This paper surveys the known properties and presents many new results for the Legendre differential expression and the associated linear differential...