Properties of k-beta function with several variables

• Autorzy: Abdur Rehman , Shahid Mubeen , Rabia Safdar , Naeem Sadiq
• Języki publikacji: EN

Abstrakty

EN

In this paper, we discuss some properties of beta function of several variables which are the extension of beta function of two variables. We define k-beta function of several variables and derive some properties of this function which are the extension of k-beta function of two variables, recently defined by Diaz and Pariguan [4]. Also, we extend the formula Γk(2z) proved by Kokologiannaki [5] via properties of k-beta function.

Słowa kluczowe

EN

k-Gamma function; k-Beta function; Several variables

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2014-05-26

zaakceptowano

2015-02-03

online

2015-05-08

Twórcy

autor

Abdur Rehman

• Department of Mathematics, University of Sargodha, Sargodha, Pakistan

autor

Shahid Mubeen

• Department of Mathematics, University of Sargodha, Sargodha, Pakistan

autor

Rabia Safdar

• Department of Mathematics, G.C.University, Faisalabad, Pakistan

autor

Naeem Sadiq

• Department of Mathematics, G.C.University, Faisalabad, Pakistan

Bibliografia

• [1] Anderson G.D., Vamanmurthy M.K., Vuorinen M.K., Conformal Invarients, Inequalities and Quasiconformal Maps, Wiley, New York, 1997
• [2] Andrews G.E., Askey R., Roy R., Special Functions Encyclopedia of Mathemaics and its Application 71, Cambridge University Press, 1999
• [3] Carlson B.C., Special Functions of Applied Mathemaics, Academic Press, New York, 1977
• [4] Diaz R., Pariguan E., On hypergeometric functions and k-Pochhammer symbol, Divulgaciones Mathematics, 2007, 15(2), 179- 192
• [5] Kokologiannaki C.G., Properties and inequalities of generalized k-gamma, beta and zeta functions, International Journal of Contemp, Math. Sciences, 2010, 5(14), 653-660
• [6] Kokologiannaki C.G., Krasniqi V., Some properties of k-gamma function, LE MATHEMATICS, 2013, LXVIII, 13-22
• [7] Krasniqi V., A limit for the k-gamma and k-beta function, Int. Math. Forum, 2010, 5(33), 1613-1617
• [8] Mansoor M., Determining the k-generalized gamma function Γk(x), by functional equations, International Journal Contemp. Math. Sciences, 2009, 4(21), 1037-1042
• [9] Mubeen S., Habibullah G.M., An integral representation of some k-hypergeometric functions, Int. Math. Forum, 2012, 7(4), 203- 207
• [10] Mubeen S., Habibullah G.M., k-Fractional integrals and applications, International Journal of Mathematics and Science, 2012, 7(2), 89-94
• [11] Mubeen S., Rehman A., Shaheen F., Properties of k-gamma, k-beta and k-psi functions, Bothalia Journal, 2014, 4, 371-379
• [12] Rainville E.D., Special Functions, The Macmillan Company, New Yark(USA), 1960
• [13] Rudin W., Real and Complex Analysis, 2nd edition McGraw-Hill, New York, 1974

Identyfikatory

DOI

10.1515/math-2015-0030