Note on the Kelvin phase functions

Philip, J. R.

doi:10.1090/S0025-5718-1979-0514829-X

Note on the Kelvin phase functions

Author: J. R. Philip
Journal: Math. Comp. 33 (1979), 337-341
MSC: Primary 33A70
DOI: https://doi.org/10.1090/S0025-5718-1979-0514829-X
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.

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