An extension of the incomplete beta function for negative integers
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, sa.2, ss.984-992, 2008 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2008
- Doi Numarası: 10.1016/j.jmaa.2007.05.075
- Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.984-992
- Hacettepe Üniversitesi Adresli: Evet
Özet
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.