대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제36권2호
  • /
  • Pages.277-298
  • /
  • 2021
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A NEW EXTENSION OF BESSEL FUNCTION

  • Chudasama, Meera H. (Department of Mathematical Sciences P. D. Patel Institute of Applied Sciences Charotar University of Science & Technology)
  • 투고 : 2020.06.13
  • 심사 : 2020.11.16
  • 발행 : 2021.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we propose an extension of the classical Bessel function by means of our ℓ-hypergeometric function [2]. As the main results, the infinite order differential equation, the generating function relation, and contour integral representations including Schläfli's integral analogue are derived. With the aid of these, other results including some inequalities are also obtained. At the end, the graphs of these functions are plotted using the Maple software.

키워드

과제정보

Author is indebted to her guide Prof. B. I. Dave, for his valuable guidance. Author sincerely thanks the referee(s) for going through the manuscript critically and giving the valuable comments of the manuscript.

참고문헌

  1. N. Barnaby and N. Kamran, Dynamics with infinitely many derivatives: the initial value problem, J. High Energy Phys. 2008 (2008), no. 2, 008, 39 pp. https://doi.org/10.1088/1126-6708/2008/02/008
  2. M. H. Chudasama and B. I. Dave, Some new class of special functions suggested by the confluent hypergeometric function, Ann. Univ. Ferrara Sez. VII Sci. Mat. 62 (2016), no. 1, 23-38. https://doi.org/10.1007/s11565-015-0238-3
  3. M. H. Chudasama and B. I. Dave, A new class of functions suggested by the generalized hypergeometric function, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 65 (2019), no. 1, 19-36.
  4. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions. Vols. I, McGraw-Hill Book Company, Inc., New York, 1953.
  5. V. Kiryakova, Generalized fractional calculus and applications, Pitman Research Notes in Mathematics Series, 301, Longman Scientific & Technical, Harlow, 1994.
  6. V. Kiryakova, Transmutation method for solving hyper-Bessel differential equations based on the Poisson-Dimovski transformation, Fract. Calc. Appl. Anal. 11 (2008), no. 3, 299-316.
  7. V. Kiryakova, From the hyper-Bessel operators of Dimovski to the generalized fractional calculus, Fract. Calc. Appl. Anal. 17 (2014), no. 4, 977-1000. https://doi.org/10.2478/s13540-014-0210-4
  8. M. Kljuchantzev, On the construction of r-even solutions of singular differential equations, Dokladi AN SSSR 224 (1975), no. 5, 1000-1008.
  9. E. D. Rainville, Special Functions, The Macmillan Co., New York, 1960.
  10. G. N. Watson, A treatise on the theory of Bessel functions, reprint of the second (1944) edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995.
  11. E. T. Whittaker and G. N. Watson, A course of modern analysis, reprint of the fourth (1927) edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. https://doi.org/10.1017/CBO9780511608759