small argument

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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 ${𝐇}_{\nu }\left(x\right)$ and ${𝐋}_{\nu }\left(x\right)$ 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 $\Vert 𝐓\Vert$ the zonal polynomial expansion given by (35.8.1) can be summed numerically. … ►See Yan (1992) for the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ 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

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$k$	nonnegative integer, except in §9.9(iii).
…
$\delta$	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.
…
$\delta$	arbitrary small positive constant.

►Unless indicated otherwise, primes denote derivatives with respect to the argument. …

8: 6.1 Special Notation

… ► ►►►

$x$	real variable.
…
$\delta$	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

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10: 7.1 Special Notation

… ► ►►►

$x$	real variable.
…
$\delta$	arbitrary small positive constant.
…

►Unless otherwise noted, primes indicate derivatives with respect to the argument. …