The generalized hypergeometric difference equation

• Autorzy: Bohner M. , Cuchta T.

Identyfikatory

DOI

10.1515/dema-2018-0007

• Języki publikacji: EN

Abstrakty

EN

A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special functions are demonstrated.

Słowa kluczowe

EN

special functions; discrete hypergeometric series; delay difference equation; contiguous relation; generalized hypergeometric functions

PL

funkcje specjalne; szeregi hipergeometryczne; równania różniczkowe; funkcje hipergeometryczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 62--75
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Bohner M.

• Department of Mathematics & Statistics, Missouri University of Science & Technology, Rolla, MO, USA 65409

autor

Cuchta T.

• Department of Computer Science and Math, Fairmont State University, Fairmont, WV, USA 26554

Bibliografia

• [1] Luke Y., The special functions and their approximations, Mathematics in Science and Engineering, Academic Press, New York-London, 1969, 53
• [2] Rainville E. D., Special functions, Chelsea Publishing Co., Bronx, N.Y., first edition, 1971
• [3] Rainville E. D., The continuous function relations for pFq with application to Batmean’s (…) and Rice’s, Bull. Am. Math. Soc., 1945, 51, 714–723
• [4] Andrews G. E., Askey R., Roy R., Special functions (Encyclopedia of Mathematics and its Applications), Cambridge University Press, Cambridge, 1999
• [5] Batchelder P. M., The hypergeometric difference equation, ProQuest LLC, Ann Arbor, MI, 1916, Thesis (Ph.D.)–Harvard University
• [6] Batchelder P. M., An introduction to linear difference equations, Dover Publications Inc., New York, 1967
• [7] Gasper G., Rahman M., Basic hypergeometric series (Encyclopedia of Mathematics and its Applications), Cambridge University Press, Cambridge, 1990
• [8] Khan M. A., Discrete hypergeometric functions and their properties, Commun. Fac. Sci. Univ. Ankara, Ser. A1, Math. Stat., 1994, 43(1-2), 31–40
• [9] Gasper G., Products of terminating 3F2(1) series, Pac. J. Math., 1975, 56, 87–95
• [10] Suslov S. K., Classical orthogonal polynomials of a discrete variable continuous orthogonality relation, Lett. Math. Phys., 1987, 14(1), 77–88
• [11] Bohner M., Peterson A., Dynamic equations on time scales - An introduction with applications, BirkhÃďuser Boston Inc., Boston, MA, 2001
• [12] Bohner M., Cuchta T., The Bessel difference equation, Proc. Amer. Math. Soc., 2017, 145(4), 1567–1580
• [13] Slavík A., Discrete Bessel functions and partial difference equations, J. Difference Equ. Appl., 2018, 24(3), 425–437

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).