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ON THE CONSTRUCTION OF (p,k)-HYPERGEOMETRIC FUNCTION AND APPLICATIONS
Fractals, 2022In this paper, we construct a [Formula: see text]-hypergeometric function by using the Hadamard product, which we call the generalized [Formula: see text]-hypergeometric function. Several properties, namely, convergence properties, derivative formulas, integral representations and differential equations are indicated of this function.
Fuli He +3 more
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Applications of Basic Hypergeometric Functions
SIAM Review, 1974This paper surveys recent applications of basic hypergeometric functions to partitions, number theory, finite vector spaces, combinatorial identities and physics.
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EXTENDED GENERALIZED τ -GAUSS’ HYPERGEOMETRIC FUNCTIONS AND THEIR APPLICATIONS
South East Asian J. of Mathematics and Mathematical Sciences, 2022In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem).
Chauhan, Bharti, Rai, Prakriti
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Formula for the Product of Gauss Hypergeometric Functions and Applications
Journal of Mathematical Sciences, 2020The \(\Gamma\)-series is defined by a lattice \(B \subset \mathbb Z^N\) and a fixed vector \(\gamma \subset \mathbb C^N\). This paper contains a formula for the product of two \(\Gamma\)-series in four variables, connected with the lattice \(B=\mathbb{Z}\langle(1,-1,-1,1)\rangle\). As a consequence of the formula for the product of \(\Gamma\)-series, a
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Applications of Hypergeometric Functions with Distribution Theory
2022Hypergeometric functions are generalized from transcendental functions. The function and series we use in quantitative economics can be evaluated analytically and expressed in form of hypergeometric function. In this paper, we introduce application of different class of hypergeometric functions in number of areas such as economic theory and econometric.
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Multiple Hypergeometric Functions and Applications
Technometrics, 1977W. R. Buckland, H. Exton
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Legendre Polynomial Expansions of Hypergeometric Functions with Applications
Journal of Mathematical Physics, 1970The expansion of a class of hypergeometric functions in a series of Legendre polynomials is derived. The range of validity and the meaning to be attached to the sums is investigated. Several applications to the problem of the scattering of charged particles are presented.
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On an application of the Kummer confluent hypergeometric functions
Conference Proceedings 2000 International Conference on Mathematical Methods in Electromagnetic Theory (Cat. No.00EX413), 2002A lemma concerning an important property of the real zeros of the Kummer function is proved numerically. Based on it and on some known attributes of the latter, criteria for slow TE/sub 0n/ mode propagation in a circular waveguide with azimuthally magnetized ferrite are drawn.
G.N. Georgiev +2 more
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Series Expansion for a Hypergeometric Function of Matrix Argument with Applications
Australian Journal of Statistics, 1982SummaryA series expansion is obtained for the confluent hypergeometric function of the second kind when the argument is a 2 times 2 positive definite matrix. Applications are made to the distributions of Hotelling's generalized T02 statistic, and the smallest latent root of the covariance matrix.
Gupta, Rameshwar D. +1 more
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Applications Involving Hypergeometric-Type Functions
1998Abstract In this final chapter we illustrate the use of the general family of hypergeometric functions in various applications. Although we have chosen specific examples from the fields of statistical communication theory, fluid mechanics, and random fields, the techniques we use are sufficiently general that they apply to a wider ...
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