Basic hypergeometric series
On Convergence of Series Involving Basic Hypergeometric Series
... called 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 ...r basic ...
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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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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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On Identities Of Rogers-Ramanujan Type
... between Basic Hypergeometric Series and with the incorporation of some identities from Lucy Slater’s famous list of 130 identities of Rogers-Ramanujan ...
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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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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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3. Some recurrence relations for the generalized basic hypergeometric functions
... We conclude with the remark that the results deduced in the present article appears to be a new contribution to the theory of basic hypergeometric series. Secondly, one can easily obtain number of ...
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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 ...
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Two Inequalities for and Applications
... called 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 ...the ...
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Vol 3, No 5 (2012)
... - series to carry out researches in this ...for 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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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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Unified integrals associated with generalized Bessel functions and Struve functions
... in [18, 19]. Properties of this GWHF were investigated in [8], (see also [10, 9]. In particular, it was proved [8] that p ψ q (z), z ∈ C is an entire function under the condition (5). Compo- sitions of GBF and GSF with ...
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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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6. Extended generalized hypergeometric functions and their applications
... [14] H. M. Srivastava, A. C ¸ etinkaya and O. Kımaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 (2014), 484–491. [15] H. M. Srivastava, M. A. ...
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Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution
... generalization belongs to the generalized power series, generalized hypergeometric fam- ilies and also arises as weighted Poisson distributions. Like the HP, COM-Poisson and generalized Poisson ...
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Multiple Integrals Involving The S Generalized Gauss's Hypergeometric Function, Class of Polynomials, Multivariable Aleph-Function and Multivariable I-Function I
... In this paper we have evaluated a generalized multiple integrals involving the multivariable Aleph-function, a class of polynomials of several variables, the S generalized Gauss hypergeometric function and the ...
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A Study of Unified Fractional Integral Operators Involving S-Generalized Gauss's Hypergeometric, Fox's H-Function and Gimel Function
... to hypergeometric and related functions, Integral Transforms and Special Functions: 23, 659683 (2012) [8] ...Gauss hypergeometric functions, Applied Mathematics and Computation 247, 348352 ...
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Reduction formulae for the Lauricella functions in several variables
... Here, in this paper, we aim mainly at showing how one can obtain several interesting reduction formulae for Lauricella functions from a multiple hypergeometric series iden- tity (.). For this, we recall ...
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A Mathematical Review on Generalized Hyper geometric Differential Equation Including 3F2 Type Function
... of hypergeometric function such as Confluent hypergeometric function, Gauss hypergeometric function, 3 F 2 type hypergeometric function, generalized hypergeometric function and obtain ...
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