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Note on the Kelvin phase functions

Author: J. R. Philip
Journal: Math. Comp. 33 (1979), 337-341
MSC: Primary 33A70
MathSciNet review: 514829
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Abstract: Both theoretical consistency and practical convenience demand that the values of the Kelvin phase functions ${\theta _n}(x)$ and ${\phi _n}(x)$ be defined uniquely and be well-ordered in n. This is achieved by taking, for $n \geqslant 0$, ${\theta _n}(0) = - {\phi _n}(0) = 3n\pi /4$. The necessary amendments to extant tables are indicated.

References [Enhancements On Off] (What's this?)

    N. W. McLACHLAN, Bessel Functions for Engineers, Clarendon Press, Oxford, 1934.
  • Bessel functions. Part IV: Kelvin functions, Royal Society Mathematical Tables, Vol. 10, Published for the Royal Society at the Cambridge University Press, New York, 1964. Prepared on behalf of The Mathematical Tables Committee by Andrew Young and Alan Kirk. MR 0164064
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Keywords: Kelvin phase functions
Article copyright: © Copyright 1979 American Mathematical Society