본문 바로가기
KERD
논문KCI 등재

A NOTE ON SOME REPRESENTATIONS OF APPELL AND HORN FUNCTION

A. BELAFHAL|E. M. EL HALBA|T. USMAN
장전수학회 (Jangjeon Mathematical Society)|2020.01|Advanced Studies in Contemporary Mathematics|제30권 제1호|pp. 5-16

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Appell functionsHorn functionsGeneralized Hypergeometric functionGamma function.
주제분류수학

초록

In the present note, we obtain certain new representations of the four Appell functions F1, F2, F3 and F4, and of the four Horn functions H1, H2, H3 and H4 in terms of series of generalized hypergeometric functions. By specializing certain parameters, some new interesting connections with generalized hypergeometric function and formulas are also obtained as special cases of our main results.

Abstract

In the present note, we obtain certain new representations of the four Appell functions F1, F2, F3 and F4, and of the four Horn functions H1, H2, H3 and H4 in terms of series of generalized hypergeometric functions. By specializing certain parameters, some new interesting connections with generalized hypergeometric function and formulas are also obtained as special cases of our main results.

참고문헌 (20)

  1. P. Appell, "Fonction hypergeometriques et hyperspheriques : Polynomes d'hermite" (1926), Gauthier Villars
  2. W. N. Bailey, "On the sum of a terminating 3F2(1)", The Quarterly Journal of Mathematics, 2, pp.237~240 (1953)
  3. Yu. A. Brychkov, "On new reduction formulas for the Humbert functions 2, 2 and 3", Integral Transform and Special Functions, 28, pp.350~360 (2017)
  4. 최준상, "CERTAIN SUMMATION FORMULAS FOR HUMBERT’S DOUBLE HYPERGEOMETRIC SERIES Ψ2 AND Φ2", 대한수학회논문집, 30(4), pp.439~446 (2015), 대한수학회
  5. R.M. Colomb, "Very fast decision table execution of propositional ex-pert systems", Proceedings of the 8th National Conference on Articial Intelligence (AAAI-90), pp.671~676 (1990)
  6. I.I. Guseinov, "Calculation of the generalized Hubbell rectangular source in-tegrals using binomial coefficients", Applied Mathematics and Computation, 161, pp.285~292 (2005)
  7. L.D. Landau, "Quantum Mechanics: Non-Relativistic Theory" (1981), Pergamon Press
  8. J.L. Madajczyk, "Singular part of the hydrogen dipole matrix element", J of Physics A: Mathematical and General, 22, pp.2369~2374 (1989)
  9. V. V. Manako, "A connection formula between double hypergeometric series 2 and 3", Inte-gral Transforms and Special Functions, 23, pp.503~508 (2012)
  10. M. Minoux, "A simplified linear-time unit resolution algorithm for Horn formulae and computer implementation", Information Processing Letters, 29, pp.1~12 (1988)
  11. T.A. Nguyen, "Checking an expert systems knowl-edge base for consistency and completeness", Proceedings of the 9th International Joint Conference on Artificial Inteligence, 29, pp.375~378 (1985)
  12. S.B. Opps, "Recursion formulas for Appells hypergeometric func-tion F2 with some applications to radiation field problems", Applied Mathematics and Compu-tation, 207, pp.545~558 (2009)
  13. A.P. Prudnikov, "Table of Integrals, Series, and Prod-ucts" (2007), Academic Press
  14. A. k. Rathie, "On a representation of Humbert's double hypergeometric series 2 in a series of Gauss's 2F1 function", ~ (2013)
  15. A.K. Rathie, "On a representation of Humbert's double hy-pergeometric series 3 in a series of Gauss's 2F1 function", ~ (2016)
  16. M. J. Schlosser, "Computer Algebra in Quantum Field Theory", pp.305~324 (2013), Springer
  17. M. A. Shpot, "A massive Feynman integral and some reduction relations for Appell func-tions", Journal of Mathematical Physics, 48, pp.123512~123525 (2007)
  18. H.M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers
  19. H.M. Srivastava, "A treatise on generating functions" (1984), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons
  20. H.M. Srivastava, "Multiple Gaussian Hypergeometric series" (1985), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons

관련 논문AI추천

Extended Lauricella and Appell Functions and Their Associated PropertiesH. M. Srivastava, M. M. Joshi, R. K. Parmar장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제2호A note on certain transformation formulas related to Appell, Horn and Kamp\'{e} de F\'{e}riet functionsArjun K. Rathie, Asmaa Orabi Mohammed, Medhat Ahmed Rakha대한수학회 · 대한수학회논문집2023 · 제38권 제3호Some integral representations and transforms for extended generalized Appell's and Lauricella's hypergeometric functions김용섭대한수학회 · 대한수학회논문집2017 · 제32권 제2호Further Hypergeometric Functions in Four Variables and Their Associated Properties김태균, J. A. Younis, P. Agarwal, S. Jain장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제3호On some formulas for the generalized Appell type functionsKottakkaran Sooppy Nisar, Mumtaz Ahmad Khan, Praveen Agarwal, Shilpi Jain대한수학회 · 대한수학회논문집2017 · 제32권 제4호The Incomplete Lauricella Functions of Several Variables and Associated Properties and Formulas최준상, H. M. Srivastava, Rakesh K. Parmar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제1호

이 간행물의 다른 논문 (12건)

RESTRICTION OF A GUICHARDET–WIGNER PSEUDOCHARACTER ON A SIMPLY CONNECTED SIMPLE HERMITIAN SYMMETRIC LIE GROUP TO A SIMPLY CONNECTED SIMPLE HERMITIAN SYMMETRIC SUBGROUPA. I. Shternpp. 1-4CERTAIN SEQUENCE SPACES USING Δ-OPERATORANTESAR ALDAWOUD, ABDUL HAMID GANIEpp. 17-27Status Sum Eigenvalues and Energy of GraphsHarishchandra S. Ramane, Ismail Naci CANGUL, Saroja Y. Talwarpp. 29-47GENERALIZED NET REPRESENTATIONS OF CONTROL STRUCTURES IN SERVICE SYSTEMS THEORYSTOYAN PORYAZOV, EMILIYA SARANOVA, VELIN ANDONOVpp. 49-60Hypergeometric functions and associated families of meromorphically starlike and convex functions조낙은, 김지아pp. 61-68
원문 보기