Some summation and Laplace transformation formulas for the Gauss hypergeometric series
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The authors derive a family of three summation formulas for the Gauss hypergeometric series 2F1 and show how their summation formulas would provide the correct forms of some erroneous hypergeometric summation theorems recorded by Prudnikov et al. [3]. By means of the correct forms of these summation theorems, the Laplace transforms of Kummer’s confluent hypergeometric function 1F1 are also presented in closed forms.
Abstract
The authors derive a family of three summation formulas for the Gauss hypergeometric series 2F1 and show how their summation formulas would provide the correct forms of some erroneous hypergeometric summation theorems recorded by Prudnikov et al. [3]. By means of the correct forms of these summation theorems, the Laplace transforms of Kummer’s confluent hypergeometric function 1F1 are also presented in closed forms.
참고문헌 (7)
- J. Choi, "A generalization of a formula due to Kummer", Integral Transforms Spec. Funct, 22, pp.851~859 (2011)
- E. E. Kummer, "Uber die hypergeometrische Reihe", J. Reine Angew. Math, 15, pp.39~83 (1836)
- E. E. Kummer, "Collected Papers, Vol. II: Function Theory, Geometry and Miscellaneous" (1975), Springer-Verlag
- A. P. Prudnikov, "Integrals and Series, Vol. 3: More Special Functions, Nauka, Moscow, 1986" (1990), Gordon and Breach Science Publishers
- M. A. Rakha, "Generalizations of classical summation theorems for the series 2F1 and 3F2 with applications", Integral Transforms Spec. Funct, 22, pp.823~840 (2011)
- H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers
- H. M. Srivastava, "A Treatise on Generating Functions", pp.10~ (1984), Halsted Press