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Communications of the Korean Mathematical Society = 대한수학회논문집 v.25 no.3, 2010년, pp.385 - 389   SCOPUS
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GENERALIZATIONS OF TWO SUMMATION FORMULAS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION OF HIGHER ORDER DUE TO EXTON

Choi, June-Sang    (DEPARTMENT OF MATHEMATICS DONGGUK UNIVERSITY   ); Rathie, Arjun Kumar    (DEPARTMENT OF MATHEMATICS VEDANT COLLEGE OF ENGINEERING AND TECHNOLOGY  );
  • 초록

    In 1997, Exton, by mainly employing a widely-used process of resolving hypergeometric series into odd and even parts, obtained some new and interesting summation formulas with arguments 1 and -1. We aim at showing how easily many summation formulas can be obtained by simply combining some known summation formulas. Indeed, we present 22 results in the form of two generalized summation formulas for the generalized hypergeometric series $_4F_3$ , including two Exton's summation formulas for $_4F_3$ as special cases.


  • 주제어

    generalized hypergeometric series $_pF_q$ .   summation theorems for $_pF_q$.  

  • 참고문헌 (9)

    1. J. Choi and H. M. Srivastava, Certain classes of infinite series, Monatsh. Math. 127 (1999), no. 1, 15?25. 
    2. W. Chu and L. de Donno, Hypergeometric series and harmonic number identities, Adv. in Appl. Math. 34 (2005), no. 1, 123?137. 
    3. H. Exton, Multiple Hypergeometric Functions and Applications, Ellis Horwood, Chichester, UK, 1976. 
    4. H. Exton, Some new summation formulae for the generalised hypergeometric function of higher order, J. Comput. Appl. Math. 79 (1997), no. 2, 183?187. 
    5. 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. 
    6. E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960. 
    7. L.-C. Shen, Remarks on some integrals and series involving the Stirling numbers and ${\zeta}(n)$, Trans. Amer. Math. Soc. 347 (1995), no. 4, 1391?1399. 
    8. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966. 
    9. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001. 

 저자의 다른 논문

  • Choi, June-Sang (133)

    1. 1992 "E.W. BARNES' APPROACH OF THE MULTIPLE GAMMA FUNCTIONS" Journal of the Korean Mathematical Society = 대한수학회지 29 (1): 127~140    
    2. 1994 "THE MULTIPLE HURWITZ ZETA FUNCTION" The Pusan Kyongnam mathematical journal 10 (1): 173~186    
    3. 1995 "FORMAL MANIPULATIONS OF DOUBLE SERIES AND THEIR APPLICATIONS" The Pusan Kyongnam mathematical journal 11 (2): 259~269    
    4. 1996 "EXPLICIT FORMULAS FOR THE GENERALIZED BERNOULLI AND EULER POLYNOMIALS" The Pusan Kyongnam mathematical journal 12 (2): 183~190    
    5. 1996 "EVALUATION OF ${\int_0}^{\frac{\pi}{4}}$ log sin t dt" The Pusan Kyongnam mathematical journal 12 (1): 35~39    
    6. 1996 "SOME IDENTITIES INVOLVING FACTORIALS" Journal of the Korean Society of Mathematical Education. 한국수학교육학회지. Series B, Pure and applied mathematics 3 (1): 41~46    
    7. 1997 "ON THE EULER'S CONSTANT" East Asian mathematical journal 13 (1): 33~41    
    8. 1997 "THE DOUBLE GAMMA FUNCTION" East Asian mathematical journal 13 (2): 159~174    
    9. 1997 "IDENTITIES INVOLVING THE HURWITZ AND RIEMANN ZETA FUNCTIONS" Communications of the Korean Mathematical Society = 대한수학회논문집 12 (2): 203~210    
    10. 1997 "A FORMULA RELATED TO FRACTIONAL CLACULUS" Communications of the Korean Mathematical Society = 대한수학회논문집 12 (2): 457~466    

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