A note on Langford’s cylinder functions 𝑐_{𝑛}(𝑧,𝑧₀) and 𝑒_{𝑛}(𝑧,𝑧₀)

Hill, James M.; Dewynne, Jeffrey N.

doi:10.1090/qam/793525

A note on Langford’s cylinder functions $c_n(z,z_0)$ and $e_n(z,z_0)$

Authors: James M. Hill and Jeffrey N. Dewynne
Journal: Quart. Appl. Math. 43 (1985), 179-185
MSC: Primary 33A40; Secondary 35C99, 80A20
DOI: https://doi.org/10.1090/qam/793525
MathSciNet review: 793525
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: New general expressions are given for Langford’s cylinder functions, which occur in solutions of the Cauchy problem for the heat equation in cylindrical co-ordinates. These formulae are deduced by means of generating functions. In addition a new technique is used to obtain Langford’s formal series, new basic formulae connecting Langford’s various cylinder functions are established and their relevance in a formal series solution of a moving boundary problem is noted.

Jeffrey N. Dewynne and James M. Hill, On an integral formulation for moving boundary problems, Quart. Appl. Math. 41 (1983/84), no. 4, 443–455. MR 724055, DOI https://doi.org/10.1090/S0033-569X-1984-0724055-3

G. A. Grinberg and O. M. Chekmarera, Motion of the phase interface in the Stefan problem, Sov. Phys. Tech. Phys. 15 (1971), 1579–1583

James M. Hill, Some unusual unsolved integral equations for moving-boundary diffusion problems, Math. Sci. 9 (1984), no. 1, 15–23. MR 750246
David Langford, New analytic solutions of the one-dimensional heat equation for temperature and heat flow rate both prescribed at the same fixed boundary (with applications to the phase change problem), Quart. Appl. Math. 24 (1967), 315–322. MR 211094, DOI https://doi.org/10.1090/S0033-569X-1967-0211094-4