A new denition of the incomplete beta function as a distribution-
valued meromorphic function is given and the finite parts of it
and of its partial derivatives at the singular values are calculated and
compared with formulas in the literature.
J. G. van der Corput: Introduction to the neutrix calculus, J. Analyse Math., 7 (1959/60), 291–398.
J. Dieudonné: Eléments d’analyse III, Chap. XVI et XVII, Gauthier-Villars, Paris (1970).
B. Fisher, M. Lin and S. Orankitjaroen: Results on partial derivatives of the incomplete beta function, Rostock Math. Kolloq., 72 (2019/20), 3–10.
I. S. Gradshteyn, I. M. Ryzhik: Table of integrals, series and products, Academic Press, New York (1980).
W. Gröbner, N. Hofreiter: Integraltafel, 2. Teil: Bestimmte Integrale, 5th edn., Springer, Wien (1973).
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).
J. Horváth: Finite parts of distributions. In: Linear operators and approximation (ed. by P. L. Butzer et al.), 142–158, Birkhäuser, Basel (1972).
S. G. Krantz: Handbook of complex variables, Birkhäuser, Boston (1999).
J. Lavoine: Calcul symbolique. Distributions et pseudo-fonctions, Editions du CNRS, Paris (1959).
N. Ortner, P. Wagner: Distribution-valued analytic functions, Tredition, Hamburg (2013).
N. Ortner, P. Wagner, Fundamental solutions of linear partial differential operators, Springer, New York (2015).
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.
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).
M. Riesz: L’intégrale de Riemann–Liouville et le problème de Cauchy, Acta Math., 81 (1948), 1–223.
L. Schwartz: Théorie des distributions, 2nd edn., Hermann, Paris (1966).
J. G. van der Corput: Introduction to the neutrix calculus, J. Analyse Math., 7 (1959/60), 291–398.
J. Dieudonné: Eléments d’analyse III, Chap. XVI et XVII, Gauthier-Villars, Paris (1970).
B. Fisher, M. Lin and S. Orankitjaroen: Results on partial derivatives of the incomplete beta function, Rostock Math. Kolloq., 72 (2019/20), 3–10.
I. S. Gradshteyn, I. M. Ryzhik: Table of integrals, series and products, Academic Press, New York (1980).
W. Gröbner, N. Hofreiter: Integraltafel, 2. Teil: Bestimmte Integrale, 5th edn., Springer, Wien (1973).
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).
J. Horváth: Finite parts of distributions. In: Linear operators and approximation (ed. by P. L. Butzer et al.), 142–158, Birkhäuser, Basel (1972).
S. G. Krantz: Handbook of complex variables, Birkhäuser, Boston (1999).
J. Lavoine: Calcul symbolique. Distributions et pseudo-fonctions, Editions du CNRS, Paris (1959).
N. Ortner, P. Wagner: Distribution-valued analytic functions, Tredition, Hamburg (2013).
N. Ortner, P. Wagner, Fundamental solutions of linear partial differential operators, Springer, New York (2015).
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.
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).
M. Riesz: L’intégrale de Riemann–Liouville et le problème de Cauchy, Acta Math., 81 (1948), 1–223.
L. Schwartz: Théorie des distributions, 2nd edn., Hermann, Paris (1966).
Ortner, N., & Wagner, P. (2022). On the singular values of the incomplete Beta function. Constructive Mathematical Analysis, 5(2), 93-104. https://doi.org/10.33205/cma.1086298
AMA
1.Ortner N, Wagner P. On the singular values of the incomplete Beta function. CMA. 2022;5(2):93-104. doi:10.33205/cma.1086298
Chicago
Ortner, Norbert, and Peter Wagner. 2022. “On the Singular Values of the Incomplete Beta Function”. Constructive Mathematical Analysis 5 (2): 93-104. https://doi.org/10.33205/cma.1086298.
EndNote
Ortner N, Wagner P (June 1, 2022) On the singular values of the incomplete Beta function. Constructive Mathematical Analysis 5 2 93–104.
IEEE
[1]N. Ortner and P. Wagner, “On the singular values of the incomplete Beta function”, CMA, vol. 5, no. 2, pp. 93–104, June 2022, doi: 10.33205/cma.1086298.
ISNAD
Ortner, Norbert - Wagner, Peter. “On the Singular Values of the Incomplete Beta Function”. Constructive Mathematical Analysis 5/2 (June 1, 2022): 93-104. https://doi.org/10.33205/cma.1086298.
JAMA
1.Ortner N, Wagner P. On the singular values of the incomplete Beta function. CMA. 2022;5:93–104.
MLA
Ortner, Norbert, and Peter Wagner. “On the Singular Values of the Incomplete Beta Function”. Constructive Mathematical Analysis, vol. 5, no. 2, June 2022, pp. 93-104, doi:10.33205/cma.1086298.
Vancouver
1.Norbert Ortner, Peter Wagner. On the singular values of the incomplete Beta function. CMA. 2022 Jun. 1;5(2):93-104. doi:10.33205/cma.1086298