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1: 4.2 Definitions
§4.2(iv) Powers
Powers with General Bases
The general a 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
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 μ and ν 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
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 λ ν ( q )
Higher coefficients can be found by equating powers of q in the following continued-fraction equation, with a = λ ν ( q ) : …
§28.15(ii) Solutions me ν ( z , q )
9: 4.6 Power Series
§4.6 Power Series
§4.6(i) Logarithms
§4.6(ii) Powers
10: 10.8 Power Series
§10.8 Power Series