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On the singular values of the incomplete Beta function

Yıl 2022, Cilt: 5 Sayı: 2, 93 - 104, 15.06.2022

Norbert Ortner Peter Wagner

https://doi.org/10.33205/cma.1086298

Öz

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.

Anahtar Kelimeler

Beta function distribution theory finite parts

Kaynakça

  • 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).

Yıl 2022, Cilt: 5 Sayı: 2, 93 - 104, 15.06.2022

Norbert Ortner Peter Wagner

https://doi.org/10.33205/cma.1086298

Öz

Kaynakça

  • 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).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Norbert Ortner

Peter Wagner

Yayımlanma Tarihi 15 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 2

Kaynak Göster

APA 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 Ortner N, Wagner P. On the singular values of the incomplete Beta function. CMA. Haziran 2022;5(2):93-104. doi:10.33205/cma.1086298
Chicago Ortner, Norbert, ve Peter Wagner. “On the Singular Values of the Incomplete Beta Function”. Constructive Mathematical Analysis 5, sy. 2 (Haziran 2022): 93-104. https://doi.org/10.33205/cma.1086298.
EndNote Ortner N, Wagner P (01 Haziran 2022) On the singular values of the incomplete Beta function. Constructive Mathematical Analysis 5 2 93–104.
IEEE N. Ortner ve P. Wagner, “On the singular values of the incomplete Beta function”, CMA, c. 5, sy. 2, ss. 93–104, 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 (Haziran 2022), 93-104. https://doi.org/10.33205/cma.1086298.
JAMA Ortner N, Wagner P. On the singular values of the incomplete Beta function. CMA. 2022;5:93–104.
MLA Ortner, Norbert ve Peter Wagner. “On the Singular Values of the Incomplete Beta Function”. Constructive Mathematical Analysis, c. 5, sy. 2, 2022, ss. 93-104, doi:10.33205/cma.1086298.
Vancouver Ortner N, Wagner P. On the singular values of the incomplete Beta function. CMA. 2022;5(2):93-104.
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