Annales Mathématiques
Blaise Pascal
no. 2
A new family of functional series relations involving digamma functions
Annales Mathématiques Blaise Pascal, Volume 3 (1996) no. 2, pp. 189-198. 
@article{AMBP_1996__3_2_189_0,
     author = {R.K. Raina and R.K. Ladda},
     title = {A new family of functional series relations involving digamma functions},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {189--198},
     publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
     volume = {3},
     number = {2},
     year = {1996},
     doi = {10.5802/ambp.76},
     zbl = {0869.33006},
     mrnumber = {1435324},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.76/}
}
TY  - JOUR
TI  - A new family of functional series relations involving digamma functions
JO  - Annales Mathématiques Blaise Pascal
PY  - 1996
DA  - 1996///
SP  - 189
EP  - 198
VL  - 3
IS  - 2
PB  - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.76/
UR  - https://zbmath.org/?q=an%3A0869.33006
UR  - https://www.ams.org/mathscinet-getitem?mr=1435324
UR  - https://doi.org/10.5802/ambp.76
DO  - 10.5802/ambp.76
LA  - en
ID  - AMBP_1996__3_2_189_0
ER  - 
%0 Journal Article
%T A new family of functional series relations involving digamma functions
%J Annales Mathématiques Blaise Pascal
%D 1996
%P 189-198
%V 3
%N 2
%I Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
%U https://doi.org/10.5802/ambp.76
%R 10.5802/ambp.76
%G en
%F AMBP_1996__3_2_189_0
R.K. Raina; R.K. Ladda. A new family of functional series relations involving digamma functions. Annales Mathématiques Blaise Pascal, Volume 3 (1996) no. 2, pp. 189-198. doi : 10.5802/ambp.76. https://ambp.centre-mersenne.org/articles/10.5802/ambp.76/

[1 ] B.N. Al-Saqabi, S.L. Kalla and H.M. Srivastava, A certain family of infinite series associated with digamma functions, J. Math. Anal. Appl. 159 (1991), 361-372. | MR: 1120938 | Zbl: 0726.33002

[2 ] B.L.J. Braaksma, Asymptotic expansions and analytical countinuations for a class of Barnes - integral, Compositio Math. 15 (1964) , 239-341. | Numdam | MR: 167651 | Zbl: 0129.28604

[3 ] C. Fox, The G and H functions as symmetrical Fourier Kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429. | MR: 131578 | Zbl: 0096.30804

[4 ] S.L. Kalla, Functional relations by means of Riemann - Liouville operator, Serdica 13 (1987), 170-173. | MR: 903439 | Zbl: 0634.33007

[5 ] S.L. Kalla and B. Al-Saqabi, A functional relation involving Ψ-function, Rev. Tech. Fac. Ingr. Univ. Zulia 8 (1985), 31-35. | MR: 824949 | Zbl: 0589.39009

[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. | MR: 985873 | Zbl: 0662.33001

[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. | MR: 860085 | Zbl: 0616.26005

[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. | MR: 1213814 | Zbl: 0896.33008

[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. | MR: 985182 | Zbl: 0651.33002

[9 a ] N.-E. Nörlund, Leçons sur les séries d'interpolation, Paris, Gauthier-Villars, 1926. | JFM: 52.0301.04

[10 ] R.K. Raina, A series relation by means of certain fractional calculus operators, Indian J. Pure Appld. Math. 21(2) (1990), 172-175. | MR: 1041940 | Zbl: 0693.33003

[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. Monthly 90 (1983) 562-566. | Zbl: 0539.26005

[12 ] B. Ross, Methods of Summation, Descrates Press, Koriyama (1987). | MR: 1012739 | Zbl: 0726.40001

[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 calculus 1 (1992), 69-74. | MR: 1165437 | Zbl: 0849.33009

[14 ] H.M. Srivastava and P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Publication (1985). | MR: 834385 | Zbl: 0552.33001

[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 Delhi and Madras (1982). | MR: 691138 | Zbl: 0506.33007

Cited by Sources: