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COMPUTING THE CONICAL FUNCTION P-1/2+iτμ (x)
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DOI：10.1137/070712006.png)
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A stable computational scheme for the conical function P--1/2+i tau(mu) (x) for x > -1, real tau, and mu <= 0 or mu is an element of N is presented. The scheme combines uniform asymptotic expansions for large vertical bar mu vertical bar with the application of the three-term recurrence relation on the mu index in the direction of decreasing vertical bar mu vertical bar when x > 0. When x < 0, the conditioning of recursion is the opposite, and conical functions can be computed in the direction of increasing vertical bar mu vertical bar.
Keyword:
Legendre functions
conical functions
hypergeometric functions
modified Bessel functions
three-term recurrence relations
difference equations
stability of recurrence relations
numerical evaluation of special functions
asymptotic analysis
期刊
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2.6
论文数:
5.1K
被引数:
1.8W
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