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1: 11.13 Methods of Computation
Then from the limiting forms for small argument (§§11.2(i), 10.7(i), 10.30(i)), limiting forms for large argument (§§11.6(i), 10.7(ii), 10.30(ii)), and the connection formulas (11.2.5) and (11.2.6), it is seen that H ν ( x ) and L ν ( x ) can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity. …
2: 35.10 Methods of Computation
§35.10 Methods of Computation
For small values of || T || the zonal polynomial expansion given by (35.8.1) can be summed numerically. … See Yan (1992) for the F 1 1 and F 1 2 functions of matrix argument in the case m = 2 , and Bingham et al. (1992) for Monte Carlo simulation on O ( m ) applied to a generalization of the integral (35.5.8). …
3: 2.5 Mellin Transform Methods
To verify (2.5.48) we may use …
4: 10.67 Asymptotic Expansions for Large Argument
5: 9.1 Special Notation
k nonnegative integer, except in §9.9(iii).
δ arbitrary small positive constant.
primes derivatives with respect to argument.
6: 10.74 Methods of Computation
The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument x or z is sufficiently small in absolute value. …
7: 11.1 Special Notation
x real variable.
δ arbitrary small positive constant.
Unless indicated otherwise, primes denote derivatives with respect to the argument. …
8: 6.1 Special Notation
x real variable.
δ arbitrary small positive constant.
Unless otherwise noted, primes indicate derivatives with respect to the argument. …
9: 10.68 Modulus and Phase Functions
With arguments ( x ) suppressed, …
§10.68(iii) Asymptotic Expansions for Large Argument
10: 7.1 Special Notation
x real variable.
δ arbitrary small positive constant.
Unless otherwise noted, primes indicate derivatives with respect to the argument. …