Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
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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.

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DOI: https://doi.org/10.1090/qam/793525
Article copyright: © Copyright 1985 American Mathematical Society

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