TY - JOUR T1 - On the singular values of the incomplete Beta function AU - Wagner, Peter AU - Ortner, Norbert PY - 2022 DA - June DO - 10.33205/cma.1086298 JF - Constructive Mathematical Analysis JO - CMA PB - Tuncer ACAR WT - DergiPark SN - 2651-2939 SP - 93 EP - 104 VL - 5 IS - 2 LA - en AB - A new denition of the incomplete beta function as a distribution-valued meromorphic function is given and the finite parts of itand of its partial derivatives at the singular values are calculated andcompared with formulas in the literature. KW - Beta function KW - distribution theory KW - finite parts CR - J. G. van der Corput: Introduction to the neutrix calculus, J. Analyse Math., 7 (1959/60), 291–398. CR - J. Dieudonné: Eléments d’analyse III, Chap. XVI et XVII, Gauthier-Villars, Paris (1970). CR - B. Fisher, M. Lin and S. Orankitjaroen: Results on partial derivatives of the incomplete beta function, Rostock Math. Kolloq., 72 (2019/20), 3–10. CR - I. S. Gradshteyn, I. M. Ryzhik: Table of integrals, series and products, Academic Press, New York (1980). CR - W. Gröbner, N. Hofreiter: Integraltafel, 2. Teil: Bestimmte Integrale, 5th edn., Springer, Wien (1973). CR - L. Hörmander: The analysis of linear partial differential operators. Vol. I (Distribution theory and Fourier analysis), Grundlehren Math. Wiss. 256, 2nd edn., Springer, Berlin (1990). CR - J. Horváth: Finite parts of distributions. In: Linear operators and approximation (ed. by P. L. Butzer et al.), 142–158, Birkhäuser, Basel (1972). CR - S. G. Krantz: Handbook of complex variables, Birkhäuser, Boston (1999). CR - J. Lavoine: Calcul symbolique. Distributions et pseudo-fonctions, Editions du CNRS, Paris (1959). CR - N. Ortner, P. Wagner: Distribution-valued analytic functions, Tredition, Hamburg (2013). CR - N. Ortner, P. Wagner, Fundamental solutions of linear partial differential operators, Springer, New York (2015). CR - E. Özçağ, İ. Ege and H. Gürçay: An extension of the incomplete beta function for negative integers, J. Math. Anal. Appl., 338 (2008), 984–992. CR - V. P. Palamodov: Distributions and harmonic analysis. In: Commutative harmonic analysis. Vol. III (Enc. Math. Sci. Vol. 72, ed. by N.K. Nikol’skij), 1–127, Springer, Berlin (1995). CR - M. Riesz: L’intégrale de Riemann–Liouville et le problème de Cauchy, Acta Math., 81 (1948), 1–223. CR - L. Schwartz: Théorie des distributions, 2nd edn., Hermann, Paris (1966). UR - https://doi.org/10.33205/cma.1086298 L1 - https://dergipark.org.tr/en/download/article-file/2303644 ER -