БЕССЕЛ-КЛИФФОРД  ФУНКЦИЯЛАРИНИНГ БАЪЗИ  УМУМЛАШМАЛАРИ ВА УЛАРНИНГ ХОССАЛАРИ

О Ахмаджонова

Scientific information

No. 2 (2020): Scientific journal of the Fergana State University

SOME GENERALIZATIONS OF BESSEL-CLIFFORD FUNCTIONS AND THEIR PROPERTIES

О Ахмаджонова ^▸^▾

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Submitted: June 22, 2023
Published: 2023-06-22

Abstract

The article describes some generalizations of the Bessel-Clifford functions and their properties.

References

Clifford W.K. On Bessel functions// Mathematical Papers.-London: Oxford Univ. Press. 1882.
Hayek.N. Perez –Acosta F. Asymptotic expressions of the Dirac delta function in terms of the Bessel- Clifford functions// Pure Appl. Math Sci.1993
Abromowitz M. Coloumb wave functions expressed in terms of Bessel- Clifford functions//J.Math. Phys.1954.
Kiryakova V. The special functions of fractional calculus as generalized fractional calculus operators of some basic functions// Comput.Math. Appl. 2010.
Witte N.S. Exact solution for the reflection and diffraction of atomic de Broglie waves by the travelling evanescent laser wave// J.Phys. A:Math.Gen.1998.
Бейтмен Г., Эрдейи А. Высшие трансцендентные функции: Функции Бесселя, функции параболического цилиндра, ортогональные многочлены. −М.: Наука, 1974.
Delerue, P. (1953). Sur le calcul symbolique `a n variables et fonctions hyperbess´eliennes (II) Annales Soc. Sci. Bruxelles, ser. 1, No 3.
Kljuchantzev, M. (1983). Singular differential operators with (r − 1) parameters and Bessel functions with vector indices (in Russian) Sibirskii Mat. Zhournal. 24, No 3.
Marichev, O. I. (1978). Method of Calculation of Integrals of Special Functions (in Russian). Minsk Nauka i Technika.
Adamchik, V. S. (1986). On the solution of the hyper-Bessel differential equation (in Russian) Diff. Uravnenia. 22, No 4.
Dimovski, I. and Kiryakova, V. (1986). Generalized Poisson transmutations and corresponding representations of hyper-Bessel functions C. R. Acad. Bulg, Sci.39, No 10.

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[1] Clifford W.K. On Bessel functions// Mathematical Papers.-London: Oxford Univ. Press. 1882.

[2] Hayek.N. Perez –Acosta F. Asymptotic expressions of the Dirac delta function in terms of the Bessel- Clifford functions// Pure Appl. Math Sci.1993

[3] Abromowitz M. Coloumb wave functions expressed in terms of Bessel- Clifford functions//J.Math. Phys.1954.

[4] Kiryakova V. The special functions of fractional calculus as generalized fractional calculus operators of some basic functions// Comput.Math. Appl. 2010.

[5] Witte N.S. Exact solution for the reflection and diffraction of atomic de Broglie waves by the travelling evanescent laser wave// J.Phys. A:Math.Gen.1998.

[6] Бейтмен Г., Эрдейи А. Высшие трансцендентные функции: Функции Бесселя, функции параболического цилиндра, ортогональные многочлены. −М.: Наука, 1974.

[7] Delerue, P. (1953). Sur le calcul symbolique `a n variables et fonctions hyperbess´eliennes (II) Annales Soc. Sci. Bruxelles, ser. 1, No 3.

[8] Kljuchantzev, M. (1983). Singular differential operators with (r − 1) parameters and Bessel functions with vector indices (in Russian) Sibirskii Mat. Zhournal. 24, No 3.

[9] Marichev, O. I. (1978). Method of Calculation of Integrals of Special Functions (in Russian). Minsk Nauka i Technika.

[10] Adamchik, V. S. (1986). On the solution of the hyper-Bessel differential equation (in Russian) Diff. Uravnenia. 22, No 4.

[11] Dimovski, I. and Kiryakova, V. (1986). Generalized Poisson transmutations and corresponding representations of hyper-Bessel functions C. R. Acad. Bulg, Sci.39, No 10.