Properties of \(k\)-beta function with several variables. (English) Zbl 1347.33006
Summary: 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 R. Díaz and E. Pariguan [Divulg. Mat. 15, No. 2, 179–192 (2007; Zbl 1163.33300)]. Also, we extend the formula \(\Gamma_{k}(2z)\) proved by C. G. Kokologiannaki [Int. J. Contemp. Math. Sci. 5, No. 13–16, 653–660 (2010; Zbl 1202.33003)] via properties of \(k\)-beta function.
MSC:
| 33B15 | Gamma, beta and polygamma functions |
| 33B20 | Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) |
| 26B35 | Special properties of functions of several variables, Hölder conditions, etc. |
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