\(q\)-Hypergeometric Series
On a New Summation Formula for 𝟐𝜓𝟐 Basic Bilateral Hypergeometric Series and Its Applications
... The summation formulae for hypergeometric series form a very interesting and useful component of the theory of basic hypergeometric series. The q-binomial theorem of Cauchy 1 is perhaps the ...
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On Convergence of Series Involving Basic Hypergeometric Series
... basic hypergeometric series, play a very important role in many fields, such as affine root systems, Lie algebras and groups, number theory, orthogonal polynomials and ...basic hypergeometric ...
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Application of Hypergeometric Series in the Inverse Moments of Special Discrete Distribution*
... generalized hypergeometric series method the high- order inverse moments and high-order inverse factorial moments of the ge- neralized geometric distribution, the Katz distribution, the Lagrangian Katz ...
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Properties of convolutions for hypergeometric series with univalent functions
... Kim and Cho Advances in Difference Equations 2013, 2013 101 http //www advancesindifferenceequations com/content/2013/1/101 R ES EA RCH Open Access Properties of convolutions for hypergeometric series[.] ...
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On some fractional q-Integral inequalities
... Rahman, Basic Hypergeometric Series , 2nd Edition, (2004), Encyclopedia of Math- ematics and Its Applications, 96, Cambridge University Press, Cambridge.. [8] F[r] ...
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Two Inequalities for and Applications
... basic hypergeometric series, plays a very important role in many fields, such as affine root systems, Lie algebras and groups, number theory, orthogonal polyno- mials, physics, and so ...ric series r φ ...
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Abstract The term "hypergeometric function" sometimes refers to the generalized hypergeometric function. In mathematics, the Gaussian or ordinary hypergeometric function
... function represented by the hypergeometric series, that includes many other special functions as special or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE). ...
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Vol 2, No 12 (2011)
... This transformation lead to various results, which play important roles in number theory and transformation theory of hypergeometric series, we show that this transform can be utilized[r] ...
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3. Hypergeometric Representation for Baskakov-Durrmeyer-Stancu type operators
... Abstract. In the present paper, we introduce and study the mixed summation- integral type operators having Baskakov and Beta basis functions in summa- tion and integration, respectively. First, we estimate moments of ...
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Reduction formulae for the Lauricella functions in several variables
... The main objective of this paper is to show how one can obtain several interesting reduction formulae for Lauricella functions from a multiple hypergeometric series identity established earlier by Jaimini ...
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Some multiple Gaussian hypergeometric generalizations of Buschman Srivastava theorem
... multiple series identities which extend and generalize theorems of Buschman, Srivastava, and ...of hypergeometric series carry over naturally and simply for these identities and provide connections ...
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On Identities Of Rogers-Ramanujan Type
... The Rogers-Ramanujan Identities have two aspects: one analytical and the other is combinatorial. In this present paper, some identities of Rogers-Ramanujan Type related to modulo 6,7 and10 has been derived by using some ...
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Vol 3, No 5 (2012)
... - series to carry out researches in this ...basic hypergeometric series 2 φ 1 , 3 φ 2 and basic bilateral hypergeometric series 2 ψ 2 , 3 ψ 3 in terms of continued ...
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Some Discussions on a Kind of Improper Integrals
... Rahman, Basic Hypergeometric Series , With a foreword by Richard Askey, Second edition, Encyclopedia of Mathematics and its Applications, 96 , Cambridge University Press, Cambridge, 2004[r] ...
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Sufficiency for Gaussian hypergeometric functions to be uniformly convex
... Gaussian hypergeometric series, Ellis Hor- wood Series: Mathematics and its Applications, Halsted Press: a division of John Wiley & Sons, New York, Chichester, Brisbane, Toronto, ...
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Generating Functions for Generalized Mock Theta Functions
... Agarwal, Certain basic hypergeometric identities asso- ciated with mock theta functions, Quart. Andrews, On basic hypergeometric series, mock theta functions and partitions (I), Qu[r] ...
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New Integral Inequalities in Quantum Calculus
... N.T., Integral inequalities of Gr¨ uss type via P´ olya-Szeg¨ o and Shisha-Mond results, East Asian Math.. R., Basic Hypergeometric Series , 2nd Edition, (2004), Encyclopedia of Mathemat[r] ...
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Multiplication and Translation Formulas for the Generalized Hypergeometric Functions and Their Applications
... Many orthogonal polynomials can be represented by the hypergeometric functions or the basic hypergeometric series. So, if we can determine the nature of coefficients of multipli- cation and ...
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Hypergeometric Functions: From One Scalar Variable to Several Matrix Arguments, in Statistics and Beyond
... various hypergeometric functions in one or two scalar ...multivariate hypergeometric functions in Statistics. Hypergeometric functions of matrix arguments are encountered in non-central matrix ...
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On quotients and differences of hypergeometric functions
... Some basic properties of this series may be found in standard handbooks, see for example [1]. For some rational triples (a, b, c), the functions F(a, b; c; x) can be expressed in terms of well-known elementary ...
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