Further hypergeometric identities deducible by fractional calculus

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참고문헌 (27)

1. B. C. Berndt, "Ramanujan's Notebooks. Parts II" (1989), Springer-Verlag
2. J. Choi, "A generalization of a formula due to Kummer", Integral Transforms Spec. Funct, 22(11), pp.851~859 (2011)
3. 최준상, "Certain hypergeometric identities deducible by using the beta integral method", 대한수학회보, 50(5), pp.1673~1681 (2013), 대한수학회
4. A. Erdelyi, "An integral equation involving Legendre polynomials", SIAM J. Appl. Math, 12, pp.15~30 (1964)
5. S. Gaboury, "Some relations involving generalized Hurwitz-Lerch zeta function obtained by means of fractional derivatives with applications to Apostol-type polynomials", Adv. Difference Equ, 2013, pp.361~ (2013)
6. A. A. Kilbas, "Theory and Applications of Fractional Differential Equations" (2006), Elsevier (North-Holland) Science Publishers
7. Y. S. Kim, "Some results for terminating ₂F₁(2) series", J. Inequal. Appl, 365, pp.1~12 (2011)
8. C. Krattenthaler, "Automatic generation of hypergeometric identities by the beta integral method", J. Comput. Appl. Math, 160(1-2), pp.159~173 (2003)
9. E. E. Kummer, "Uber die hypergeometrische Reihe 1+αβ", 1⋅γ x+α(α+1)⋅β(β+1), J. Reine Angew. Math, pp.1836, 15(39-83)[DOI]
10. J.-L. Lavoie, "Fundamental properties of fractional derivatives via Pochhammer integrals" (1975), Springer-Verlag
11. J. Liouville, "Memoire sur le calcul des differentielles a indices quelconques", J. de l'Ecole Polytechnique, 13, pp.71~162 (1832)
12. K. S. Miller, "An Introduction to the Fractional Calculus and Fractional Differential Equations" (1993), John Wiley and Sons
13. T. J. Osler, "Fractional derivatives of a composite function", SIAM J. Math. Anal, 1, pp.288~293 (1970)
14. T. J. Osler, "Leibniz rule for fractional derivatives and an application to innite series", SIAM J. Appl. Math, 18, pp.658~674 (1970)
15. T. J. Osler, "Leibniz rule, the chain rule and Taylor's theorem for fractional derivatives", PhD, pp.1970
16. T. J. Osler, "Fractional derivatives and Leibniz rule", Math. Monthly, 78, pp.645~649 (1970)
17. E. D. Rainville, "Special Functions" (1960), Macmillan Company
18. M. Riesz, "L'integrale de Riemann-Liouville et le probleme de Cauchy", Acta. Math, 81, pp.1~223 (1949)
19. H. M. Srivastava, "Series Associated with Zeta and Related Functions" (2001), Kluwer Academic Publishers
20. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers
21. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series", Halsted Press (Ellis Horwoor Limited) (1985)
22. R. Tremblay, "Une contribution a la theorie de la derivee fractionnaire", PhD, pp.1974
23. R. Tremblay, "The use of fractional derivatives to expand analytical functions in terms of quadratic functions with applications to special functions", Appl. Math. Comput, 187(1), pp.507~529 (2007)
24. R. Tremblay, "A new leibniz rule and its integral analogue for fractional derivatives", Integral Transforms Spec. Funct, 24(2), pp.111~128 (2013)
25. R. Tremblay, "A new transformation formula for fractional derivatives with applications", Integral Transforms Spec. Funct, 24(3), pp.172~186 (2013)
26. R. Tremblay, "Taylor-like expansion in terms of a rational function obtained by means of fractional derivatives", Integral Transforms Spec. Funct, 24(1), pp.50~64 (2013)
27. C. Wei, "Certain transformations for multiple hypergeometric functions", Adv. Difference Equ, 360, pp.1~13 (2013)

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