JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CERTAIN HYPERGEOMETRIC IDENTITIES DEDUCIBLE BY USING THE BETA INTEGRAL METHOD
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CERTAIN HYPERGEOMETRIC IDENTITIES DEDUCIBLE BY USING THE BETA INTEGRAL METHOD
Choi, Junesang; Rathie, Arjun K.; Srivastava, Hari M.;
  PDF(new window)
 Abstract
The main objective of this paper is to show how one can obtain eleven new and interesting hypergeometric identities in the form of a single result from the old ones by mainly employing the known beta integral method which was recently introduced and used in a systematic manner by Krattenthaler and Rao [6]. The results are derived with the help of a generalization of a well-known hypergeometric transformation formula due to Kummer. Several identities including one obtained earlier by Krattenthaler and Rao [6] follow as special cases of our main results.
 Keywords
generalized hypergeometric function ;Gamma function;Pochhammer symbol;Beta integral method;Kummer's formula;generalization of Kummer's formula;
 Language
English
 Cited by
1.
FURTHER HYPERGEOMETRIC IDENTITIES DEDUCIBLE BY FRACTIONAL CALCULUS,;;

대한수학회논문집, 2014. vol.29. 3, pp.429-437 crossref(new window)
2.
TWO GENERAL HYPERGEOMETRIC TRANSFORMATION FORMULAS,;;

대한수학회논문집, 2014. vol.29. 4, pp.519-526 crossref(new window)
3.
Reduction Formulas for Srivastava's Triple Hypergeometric Series F(3)[x, y, z],;;;

Kyungpook mathematical journal, 2015. vol.55. 2, pp.439-447 crossref(new window)
1.
Remark on certain transformations for multiple hypergeometric functions, Advances in Difference Equations, 2014, 2014, 1, 126  crossref(new windwow)
2.
FURTHER HYPERGEOMETRIC IDENTITIES DEDUCIBLE BY FRACTIONAL CALCULUS, Communications of the Korean Mathematical Society, 2014, 29, 3, 429  crossref(new windwow)
3.
TWO GENERAL HYPERGEOMETRIC TRANSFORMATION FORMULAS, Communications of the Korean Mathematical Society, 2014, 29, 4, 519  crossref(new windwow)
4.
Reduction Formulas for Srivastava's Triple Hypergeometric Series F(3)[x, y, z], Kyungpook mathematical journal, 2015, 55, 2, 439  crossref(new windwow)
5.
Certain transformations for multiple hypergeometric functions, Advances in Difference Equations, 2013, 2013, 1, 360  crossref(new windwow)
 References
1.
W. N. Bailey, Generalized Hypergeometric Series, Cambridge Tracts in Mathematics and Mathematical Physics, Vol. 32, Cambridge University Press, Cambridge, London and New York, 1935; Reprinted by Stechert-Hafner Service Agency, New York and London, 1964.

2.
B. C. Berndt, Ramanujan's Notebooks. Part II, Springer-Verlag, Berlin, Heidelberg and New York, 1989.

3.
J. Choi and A. K. Rathie, Two formulas contiguous to a quadratic transformation due to Kummer with an application, Hacet. J. Math. Stat. 40 (2011), no. 6, 885-894.

4.
J. Choi, A. K. Rathie, and H. M. Srivastava, A generalization of a formula due to Kummer, Integral Transforms Spec. Funct. 22 (2011), no. 11, 851-859. crossref(new window)

5.
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vols. I, II, McGraw-Hill Book Company, New York, Toronto and London, 1953.

6.
C. Krattenthaler and K. S. Rao, Automatic generation of hypergeometric identities by the beta integral method, J. Comput. Appl. Math. 160 (2003), no. 1-2, 159-173. crossref(new window)

7.
E. E. Kummer, Uber die hypergeometrische Reihe $1+\frac{{\alpha\cdot\beta}}{{1{\cdot}}{\gamma}}x$+${\frac{{\alpha}({\alpha}+1){\cdot}{\beta}({\beta}+1)}{{1{\cdot}2{\cdot}{\gamma}({\gamma+1})}}x^2+{\cdot}{\cdot}{\cdot}$, J. Reine Angew. Math. 15 (1836), 39-83 and 127-172.

8.
J.-L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_3F_2$, J. Comput. Appl. Math. 72 (1996), no. 2, 293-300. crossref(new window)

9.
E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.

10.
H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.