호남수학학술지 (Honam Mathematical Journal)

  • 제33권2호
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  • Pages.187-206
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  • 2011
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

  • Lee, Dong-Myung (Department of Mathematics Education, Wonkwang University) ;
  • Rathie, Arjun K. (Department of Mathematics, Vedant College of Engineering & Technology) ;
  • Parmar, Rakesh K. (Department of Mathematics, Govt. College of Engineering & Technolgy) ;
  • Kim, Yong-Sup (Department of Mathematics Education, Wonkwang University)
  • 투고 : 2011.03.15
  • 심사 : 2011.04.27
  • 발행 : 2011.06.25
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초록

The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.

키워드

참고문헌

  1. M. A. Chaudhry, S. M. Zubair, Generalized incomplete gamma function with applications, J. Comput. Appl. Math. 55 (1994), 99-124. https://doi.org/10.1016/0377-0427(94)90187-2
  2. M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler's beta function, J. Comput. Appl. Math. 78 (1997), 19-32. https://doi.org/10.1016/S0377-0427(96)00102-1
  3. M. A. Chaudhry, S. M. Zubair, On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms, J. Comput. appl. Math. 59 (1995), 253-284 https://doi.org/10.1016/0377-0427(94)00026-W
  4. M. A. Chaudhry, N. M. Temme, E. J. M. Veling, Asymptotic and closed form of a generalized incomplete gamma function, J. Comput. Appl. Math. 67 (1996), 371-379. https://doi.org/10.1016/0377-0427(95)00018-6
  5. M. A. Chaudhry, S. M. Zubair, Extended incomplete gamma functions with applications, J. Math. Anal. Appl. 274 (2002), 725-745. https://doi.org/10.1016/S0022-247X(02)00354-2
  6. M. A. Chaudhry, A. Qadir, H. M. Srivastava, R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput, 159 (2004), 589-602. https://doi.org/10.1016/j.amc.2003.09.017
  7. M. A. Chaudhry, S. M. Zubair, On a class of incomplete gamma functions with applications, CRC Press (Chapman and Hall), Boca Raton, FL, 2002.
  8. A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of integral transforms, Vol. I, McGraw-Hill, New York, 1954.
  9. E.D. Rainville, Special functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  10. L. J. Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966.

피인용 문헌

  1. A NOTE ON GENERALIZED EXTENDED WHITTAKER FUNCTION vol.38, pp.2, 2016, https://doi.org/10.5831/HMJ.2016.38.2.325
  2. Extended Riemann-Liouville type fractional derivative operator with applications vol.15, pp.1, 2017, https://doi.org/10.1515/math-2017-0137
  3. Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions vol.2014, 2014, https://doi.org/10.1155/2014/735946
  4. Some results on the extended beta and extended hypergeometric functions vol.248, 2014, https://doi.org/10.1016/j.amc.2014.09.110
  5. SOME INTEGRAL TRANSFORMS AND FRACTIONAL INTEGRAL FORMULAS FOR THE EXTENDED HYPERGEOMETRIC FUNCTIONS vol.31, pp.3, 2016, https://doi.org/10.4134/CKMS.c150213
  6. EXTENDED HYPERGEOMETRIC FUNCTIONS OF TWO AND THREE VARIABLES vol.30, pp.4, 2015, https://doi.org/10.4134/CKMS.2015.30.4.403
  7. Weighted hypergeometric functions and fractional derivative vol.2017, pp.1, 2017, https://doi.org/10.1186/s13662-017-1165-7
  8. Certain Fractional Integral Operators and Extended Generalized Gauss Hypergeometric Functions vol.55, pp.3, 2015, https://doi.org/10.5666/KMJ.2015.55.3.695
  9. Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions vol.40, pp.1, 2017, https://doi.org/10.1002/mma.3986
  10. Further extended Caputo fractional derivative operator and its applications vol.24, pp.4, 2017, https://doi.org/10.1134/S106192081704001X