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ON PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS

CHOI, JUNE-SANG    (Department of Mathematics College of Natural Sciences Dongguk University   ); RATHIE ARJUN K.    (Department of Mathematics Dungar College   ); BHOJAK BHARTI    (Department of Mathematics Dungar College  );
  • 초록

    Five results closely related to the well-known Preece's identity obtained earlier by Choi and Rathie will be derived here by using some known hypergeometric identities. In addition to this, the identities obtained earlier by Choi and Rathie have also been written in a compact form.


  • 주제어

    generalized hypergeometric series $_pF_q$ .   Dixon's summation formula for $_3F_2$ .   Whipple's summation theorem for a $_3F_2$.  

  • 참고문헌 (11)

    1. W. N. Bailey, Products of generalized hypergeometric series, Proc. London Math. Soc.(2) 28 (1928), 242-254 
    2. Y. S. Kim and A. K. Rathie, A generalization of Preece's identity, Commun. Korean Math. Soc. 14 (1999), 217-222 
    3. E. E. Kummer, Uber die hypergeometrische Reihe F(a; b; x), J. Reine Angew. Math. 15 (1836), 39-83 
    4. J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Watson's theorem on the sum of a $_3F_2$, Indian J. Math. 34 (1992), 23-32 
    5. J. L. Lavoie, F. Grondin, A. K. Rathie, and K. Arora, Generalizations of Dixon's theorem on the sum of a $_3F_2$, Math. Comp. 49 (1987), 269-274 
    6. E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960 
    7. A. K. Rathie and J. Choi, A note on an identity due to Preece, Far East J. Math. Sci. 6 (1998), 205-209 
    8. A. K. Rathie, A note on generalizations of Preece's identity and other contiguous results, Bull. Korean Math. Soc. 35 (1998), 339-344 
    9. A. K. Rathie and S. Sharma, On a generalization of Preece's identity, Acta Cienc. Indica Math. 105 (1999), 167-168 
    10. C. T. Preece, The product of two generalized hypergeometric functions, Proc. London Math. Soc.(2) 24 (1924), 370-380 
    11. A. K. Rathie, A short proof of Preece's identity and other contiguous results, Rev. Mat. Estatist.(Brazil) 15 (1997), 207-210 

 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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