Closed-form summations of certain hypergeometric-type series containing the digamma function
Abstract
Recently, interesting novel summation formulae for hypergeometric-type series containing a digamma function as a factor have been established by Miller (2006 J. Phys. A: Math. Gen. 39 3011 - 20) mainly by exploiting already known results and using certain transformation and reduction formulae in the theory of the Kampe de Feriet double hypergeometric function. It is shown here that these, and several other series of this type, can be closed-form summed by simpler and more direct arguments based only on a derivative formula for the Pochhammer symbol and the theory of the digamma ( or.) function and generalized hypergeometric function. In addition, a new reduction formula for the Kamp e de Feriet function F 1:1;0 (1 2;1) [z, z] is obtained.
Source:
Journal of Physics. A: Mathematical and Theoretical, 2008, 41, 45Funding / projects:
- Ortogonalni sistemi i primene (RS-MESTD-MPN2006-2010-144004)
DOI: 10.1088/1751-8113/41/45/455205
ISSN: 1751-8113
WoS: 000260187500007
Scopus: 2-s2.0-58149354191
Collections
Institution/Community
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2008 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3546 AB - Recently, interesting novel summation formulae for hypergeometric-type series containing a digamma function as a factor have been established by Miller (2006 J. Phys. A: Math. Gen. 39 3011 - 20) mainly by exploiting already known results and using certain transformation and reduction formulae in the theory of the Kampe de Feriet double hypergeometric function. It is shown here that these, and several other series of this type, can be closed-form summed by simpler and more direct arguments based only on a derivative formula for the Pochhammer symbol and the theory of the digamma ( or.) function and generalized hypergeometric function. In addition, a new reduction formula for the Kamp e de Feriet function F 1:1;0 (1 2;1) [z, z] is obtained. T2 - Journal of Physics. A: Mathematical and Theoretical T1 - Closed-form summations of certain hypergeometric-type series containing the digamma function VL - 41 IS - 45 DO - 10.1088/1751-8113/41/45/455205 ER -
@article{ author = "Cvijović, Đurđe", year = "2008", abstract = "Recently, interesting novel summation formulae for hypergeometric-type series containing a digamma function as a factor have been established by Miller (2006 J. Phys. A: Math. Gen. 39 3011 - 20) mainly by exploiting already known results and using certain transformation and reduction formulae in the theory of the Kampe de Feriet double hypergeometric function. It is shown here that these, and several other series of this type, can be closed-form summed by simpler and more direct arguments based only on a derivative formula for the Pochhammer symbol and the theory of the digamma ( or.) function and generalized hypergeometric function. In addition, a new reduction formula for the Kamp e de Feriet function F 1:1;0 (1 2;1) [z, z] is obtained.", journal = "Journal of Physics. A: Mathematical and Theoretical", title = "Closed-form summations of certain hypergeometric-type series containing the digamma function", volume = "41", number = "45", doi = "10.1088/1751-8113/41/45/455205" }
Cvijović, Đ.. (2008). Closed-form summations of certain hypergeometric-type series containing the digamma function. in Journal of Physics. A: Mathematical and Theoretical, 41(45). https://doi.org/10.1088/1751-8113/41/45/455205
Cvijović Đ. Closed-form summations of certain hypergeometric-type series containing the digamma function. in Journal of Physics. A: Mathematical and Theoretical. 2008;41(45). doi:10.1088/1751-8113/41/45/455205 .
Cvijović, Đurđe, "Closed-form summations of certain hypergeometric-type series containing the digamma function" in Journal of Physics. A: Mathematical and Theoretical, 41, no. 45 (2008), https://doi.org/10.1088/1751-8113/41/45/455205 . .