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1: 4.2 Definitions

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§4.2(iv) Powers

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Powers with General Bases

►The general $a^{\mathrm{th}}$ power of $z$ is defined by …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. …

3: 6.6 Power Series

§6.6 Power Series

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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). …

6: 24.20 Tables

§24.20 Tables

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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 $q$

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§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 $a={\lambda }_{\nu }\left(q\right)$: … ►

§28.15(ii) Solutions ${\mathrm{me}}_{\nu }(z,q)$

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9: 4.6 Power Series

§4.6 Power Series

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§4.6(i) Logarithms

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§4.6(ii) Powers

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10: 10.8 Power Series

§10.8 Power Series

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