Pochhammer, Gamma, Beta and Hypergeometric functions
11. On the Hypergeometric Matrix $k$-Functions
... special functions encountered in physics, engineering, analytic func- tions and probability theory are special cases of hypergeometric functions ([12, ...matrix functions appear in the ...
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Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant
... This is done in full awareness that the article might thus appear a mere compilation of formulae, but our aim is to prevent it from becoming overly lengthy. Note that we can only conjecture the results for the oc- tonion ...
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A New Extension of Beta and Hypergeometric Functions
... defined beta function such as integral repre- sentations, summation formulas and Mellin ...extended beta distribu- tion and its mean, variance and moment generating function with the help of extension of ...
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CiteSeerX — Generalization of Extended Beta Function, Hypergeometric and Confluent Hypergeometric Functions
... extended beta function, extended hypergeometric and con- fluent hypergeometric function introduced by Chaudhry et ...of beta func- tion, Mellin transform, beta distribution, ...
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Inequalities of extended beta and extended hypergeometric functions
... Abstract We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric ...
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A new Generalization of Extended Beta and Hypergeometric Functions
... extended beta function and its various properties, integral representations and distribution are given in this ...extended hypergeometric and confluent hypergeometric functions using the newly ...
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Factorial, Gamma and Beta Functions
... (1.2) and the gamma function (Euler’s integral of the second kind). Γ(z) = (z − 1)! (1.3) While it is relatively easy to compute the factorial function for small integers, it is easy to see how manually computing ...
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Hypergeometric Functions
... the hypergeometric function to a finite polynomial, in which case the gamma prefactor of either G-function vanishes and the parameter sets of the G-functions violate the requirement ak − bj ≠ 1, 2, 3, ...
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Some inequalities for the $q,k$-Gamma and Beta functions
... known Gamma function was initially introduced by Thomae [11] and later deeply studied by Jackson ...k-generalized Gamma and Beta functions and they proved integral representations for Γ q,k ...
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A STUDY ON NOVEL EXTENSIONS FOR THE -ADIC GAMMA AND -ADIC BETA FUNCTIONS
... p-adic gamma function which is …rstly described by Yasou Morita in about 1975 ...p-adic gamma function is principally motivated by their importance in p-adic ...
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On some inequalities for Beta and Gamma functions via some classical inequalities
... Wang, A new inequality of Ostrowski’s type in L1 norm and applications to some special means and to some numerical quadrature rules , Tamkang J.. 3, 299–304.[r] ...
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Some inequalities involving k gamma and k beta functions with applications
... 1 Introduction In this section, we present some fundamental relations for k-gamma and k-beta functions introduced by the researchers [–]. The second and third section is devoted to the appli- ...
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Inequalities involving hypergeometric and related functions
... the hypergeometric function at the point ...are functions of the distribution’s terminal ...two hypergeometric functions depend on terminal and initial ...the hypergeometric ...
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Certain transformations for multiple hypergeometric functions
... hypergeometric functions, which are obtained with the help of the relations of Appell, Humbert, Horn and Srivastava’s multiple hypergeometric ...the beta integral method which has been ...
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Weighted hypergeometric functions and fractional derivative
... 4. Agarwal, P, Koul, CL: On generating functions. J. Rajasthan Acad. Phys. Sci. 2(3), 173-180 (2003) 5. Ozergin, E: Some properties of hypergeometric functions. Ph.D. thesis, Eastern Mediterranean ...
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Evaluation of integrals with hypergeometric and logarithmic functions
... terms, finally arriving at the relation (10). The integral identity (9) is obtained by the Beta method as described in Lemma 1.1 and details will not be outlined. A slightly different re-arrangement of the terms ...
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Hypergeometric Functions: Application in Distribution Theory
... Hypergeometric functions are able to occur in fractional calculus ...these functions is in data ...incomplete gamma, Gauss hypergeometric function or other relevant ...
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Some inequalities involving k gamma and k beta functions with applications II
... Keywords: k-gamma; k-beta; inequalities; probability distribution 1 Introduction In this section, we present some fundamental relations for k-gamma and k-beta functions introduced in ...
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Inequalities for Beta and Gamma Functions Via Some Classical and New Integral Inequalities
... SOME CLASSICAL AND NEW INTEGRAL INEQUALITIES S. S. DRAGOMIR, R. P. AGARWAL, AND N. S. BARNETT Abstract. In this survey paper we present the natural application of cer- tain integral inequalities such as, Chebychev’s ...
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Remark on certain transformations for multiple hypergeometric functions
... 2 Pochhammer contour integral representation for fractional derivative and a new generalized Leibniz rule The use of a contour of integration in the complex plane provides a very powerful tool in both classical ...
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