J Joop Boersma

Asymptotic expansion of a class of Fermi-Dirac integrals

A procedure is presented for obtaining the complete asymptotic expansion of a class of fractional integrals (of Riemann–Liouville type), in which the integrand contains the product of two derivatives of the Fermi–Dirac integral. The procedure uses two-sided Laplace transforms and Abelian asymptotics of the inverse Laplace transform. The fractional integrals considered arise in various problems from statistical mechanics and solid state physics.

Two Integrals Arising from a Reaction-Diffusion Problem (John Billingham)

Solution by J. BOERSMA AND P. J. DE DOELDER (Eindhoven University of Technology, Eindhoven, the Netherlands). The two integrals are evaluated by a method due to Belevitch [1, 3], for obtaining indefinite integrals involving independent solutions of a linear differential equation, by means of the Wronskian. First we express A,, (s) in terms of confluent hypergeometric functions [2, 6.1] and of the Hermite polynomial H, by means of [2, form. 10.13(17), (18)], viz.

Solution to problem 77-20 : When is the modified Bessel function equal to its derivative?

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publishers website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.