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1: 4.2 Definitions
Powers with General Bases
The principal value is … …
2: 12.18 Methods of Computation
These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions. …
4: 16.25 Methods of Computation
Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. …
5: 14.32 Methods of Computation
In particular, for small or moderate values of the parameters $\mu$ and $\nu$ the power-series expansions of the various hypergeometric function representations given in §§14.3(i)14.3(iii), 14.19(ii), and 14.20(i) can be selected in such a way that convergence is stable, and reasonably rapid, especially when the argument of the functions is real. In other cases recurrence relations (§14.10) provide a powerful method when applied in a stable direction (§3.6); see Olver and Smith (1983) and Gautschi (1967). …
7: 27.20 Methods of Computation: Other Number-Theoretic Functions
To calculate a multiplicative function it suffices to determine its values at the prime powers and then use (27.3.2). …
8: 28.15 Expansions for Small $q$
§28.15(i) Eigenvalues $\lambda_{\nu}\left(q\right)$
Higher coefficients can be found by equating powers of $q$ in the following continued-fraction equation, with $a=\lambda_{\nu}\left(q\right)$: …