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On Partial Derivatives Of The Incomplete Beta Function
The incomplete beta function B(x) (a, b) is defined for a, b > 0 and 0 < x < 1 and its definition was extended to negative integer values of a and b in [E. Ozcag, I. Ege, H. Gurcay, An extension of the incomplete beta function for negative integers, J. Math. Anal. Appl., in press (doi:10.1016/j.jmaa.2007.05.075)]. In this work we define the partial derivatives of the incomplete beta function B(x) (a, b) for negative integer values of a and b. (C) 2007 Elsevier Ltd. All rights reserved.WoSScopu
An Extension of the Incomplete Beta Function For Negative Integers
The incomplete beta function B-x(a, b) is defined for a, b > 0 and 0 < x < 1. Its definition can be extended, by regularization, to negative non-integer values of a and b. In this paper we define the incomplete beta function Bx (a, b) for negative integer values of a and b. Further we prove that the function partial derivative(m+n)/partial derivative a(m)partial derivative b(n)B(x)(a, b) exists for m, n = 0, 1, 2,... and all a and b. (C) 2007 Elsevier Inc. All rights reserved.WoSScopu