Asymptotic expansions and converging factors III. Gamma, psi and polygamma functions, and Fermi-Dirac and Bose-Einstein integrals
- 22 April 1958
- journal article
- research article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 244 (1239) , 484-490
- https://doi.org/10.1098/rspa.1958.0056
Abstract
Following the methods described in the first two papers (I and II) of this series, the divergent parts of the asymptotic expansions of the functions indicated in the title are replaced by easily calculable series involving one or other of the four ‘basic converging factors’ which were investigated and tabulated in I.This publication has 5 references indexed in Scilit:
- The Fermi-Dirac integrals $$\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon $$Applied Scientific Research, Section B, 1957
- On Bose-Einstein FunctionsProceedings of the Physical Society. Section A, 1954
- The computation of Fermi-Dirac functionsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1938
- LII.The “converging factor” in asymptotic series and the calculation of Bessel, laguerre and other functionsJournal of Computers in Education, 1937
- Recherches sur quelques séries semi-convergentesAnnales Scientifiques de lʼÉcole Normale Supérieure, 1886