On an Extension of Extended Beta and Hypergeometric Functions
نویسندگان
چکیده
Abstract. Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically investigate several properties of each of these extended functions, such as their various integral representations, Mellin transforms, derivatives, transformations, summation formulas, generating function and asymptotics. Relevant connections of certain special cases of the main results presented herewith are also pointed out.
منابع مشابه
Inequalities of extended beta and extended hypergeometric functions
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 functions are deduced by using the inequalities on extended beta functions. The particular cases of those results also give the Turán-type inequalities for extended confluent and extended Gaussian hypergeomet...
متن کاملA New Generalization of Extended Beta and Hypergeometric Functions
Abstract: A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and confluent hypergeometric functions using the newly extended beta function. Some properties of these extended and confluent hypergeometric functions such as integral repr...
متن کاملA Subclass of Analytic Functions Associated with Hypergeometric Functions
In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
متن کاملON AN EXTENSION OF A QUADRATIC TRANSFORMATION FORMULA DUE TO GAUSS
The aim of this research note is to prove the following new transformation formula begin{equation*} (1-x)^{-2a},_{3}F_{2}left[begin{array}{ccccc} a, & a+frac{1}{2}, & d+1 & & \ & & & ; & -frac{4x}{(1-x)^{2}} \ & c+1, & d & & end{array}right] \ =,_{4}F_{3}left[begin{array}{cccccc} 2a, & 2a-c, & a-A+1, & a+A+1 & & \ & & & & ; & -x \ & c+1, & a-A, & a+A & & end{array} right], end{equation*} wher...
متن کاملA (p, V )-extension of Hurwitz-lerch Zeta Function and Its Properties
In this paper, we define a (p, v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results. keywords...
متن کامل