A new family of functional series relations involving digamma functions

R.K. Raina; R.K. Ladda

Annales mathématiques Blaise Pascal (1996)

  • Volume: 3, Issue: 2, page 189-198
  • ISSN: 1259-1734

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Raina, R.K., and Ladda, R.K.. "A new family of functional series relations involving digamma functions." Annales mathématiques Blaise Pascal 3.2 (1996): 189-198. <http://eudml.org/doc/79164>.

@article{Raina1996,
author = {Raina, R.K., Ladda, R.K.},
journal = {Annales mathématiques Blaise Pascal},
keywords = {digamma functions; series relations; H-function},
language = {eng},
number = {2},
pages = {189-198},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {A new family of functional series relations involving digamma functions},
url = {http://eudml.org/doc/79164},
volume = {3},
year = {1996},
}

TY - JOUR
AU - Raina, R.K.
AU - Ladda, R.K.
TI - A new family of functional series relations involving digamma functions
JO - Annales mathématiques Blaise Pascal
PY - 1996
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 3
IS - 2
SP - 189
EP - 198
LA - eng
KW - digamma functions; series relations; H-function
UR - http://eudml.org/doc/79164
ER -

References

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  2. [2 ] B.L.J. Braaksma, Asymptotic expansions and analytical countinuations for a class of Barnes - integral, Compositio Math.15 (1964) , 239-341. Zbl0129.28604MR167651
  3. [3 ] C. Fox, The G and H functions as symmetrical Fourier Kernels, Trans. Amer. Math. Soc.98 (1961), 395-429. Zbl0096.30804MR131578
  4. [4 ] S.L. Kalla, Functional relations by means of Riemann - Liouville operator, Serdica13 (1987), 170-173. Zbl0634.33007MR903439
  5. [5 ] S.L. Kalla and B. Al-Saqabi, A functional relation involving Ψ-function, Rev. Tech. Fac. Ingr. Univ. Zulia8 (1985), 31-35. Zbl0589.39009MR824949
  6. [6 ] S.L. Kalla and B. Al-Saqabi, Summation of certain infinite series with digamma functions, C.R. Acad. Bulgare Sci.41 (11) (1988), 15-17. Zbl0662.33001MR985873
  7. [7 ] S.L. Kalla and B. Ross, The development of functional relations by means of fractional calculus, in Fractional Calculus, Pitman Ad. Publishing Program Boston (1985), 32-43. Zbl0616.26005MR860085
  8. [8 ] K. Nishimoto and R.K. Saxena, An application of Riemann - Liouville operator in the unification of certain functional relations, J. College Engrg. Nihhon Univ.32 (1991), 133-139. Zbl0896.33008MR1213814
  9. [9 ] K. Nishimoto and H.M. Srivastava, Certain class of infinite series summable by means of fractional calculus, J. College Engrg. Nihon Univ.30 (1989), 97-106. Zbl0651.33002MR985182
  10. [9 a ] N.-E. Nörlund, Leçons sur les séries d'interpolation, Paris, Gauthier-Villars, 1926. JFM52.0301.04
  11. [10 ] R.K. Raina, A series relation by means of certain fractional calculus operators, Indian J. Pure Appld. Math.21(2) (1990), 172-175. Zbl0693.33003MR1041940
  12. [11 ] B. Ross, Serendipidity in maths or how one is led to discover that ∑ ∞ n=1 ((1.3.5...(2n-1))/(n.2n.n!)) = ((1/2) + (3/16) + (15/144) + ...) = ln4, Amer. Math. Monthly90 (1983) 562-566. Zbl0539.26005
  13. [12 ] B. Ross, Methods of Summation, Descrates Press, Koriyama (1987). Zbl0726.40001MR1012739
  14. [13 ] H.M. Srivastava and K. Nishimoto, An elementary proof of a generalization of a certain functional relations derived by means of fractional calculus, J. Fractional calculus1 (1992), 69-74. Zbl0849.33009MR1165437
  15. [14 ] H.M. Srivastava and P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Publication (1985). Zbl0552.33001MR834385
  16. [15 ] H.M. Srivastava , K.C. Gupta and S.P. Goyal, The H functions of One and Two Variables with Applications, South Asian Publishers, New Delhiand Madras (1982). Zbl0506.33007MR691138

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