expansions in series of

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1: 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: 13.24 Series
§13.24(i) ExpansionsinSeries of Whittaker Functions
For expansions of arbitrary functions in series of $M_{\kappa,\mu}\left(z\right)$ functions see Schäfke (1961b).
6: 8.7 Series Expansions
§8.7 SeriesExpansions
8.7.6 $\Gamma\left(a,x\right)=x^{a}e^{-x}\sum_{n=0}^{\infty}\frac{L^{(a)}_{n}\left(x% \right)}{n+1},$ $x>0$, $\Re a<\frac{1}{2}$.
For an expansion for $\gamma\left(a,ix\right)$ in series of Bessel functions $J_{n}\left(x\right)$ that converges rapidly when $a>0$ and $x$ ($\geq 0$) is small or moderate in magnitude see Barakat (1961).
7: 28.11 Expansions in Series of Mathieu Functions
§28.11 ExpansionsinSeries of Mathieu Functions
28.11.7 $\sin(2m+2)z=\sum_{n=0}^{\infty}B_{2m+2}^{2n+2}(q)\operatorname{se}_{2n+2}\left% (z,q\right).$
10: 16.10 Expansions in Series of ${{}_{p}F_{q}}$ Functions
§16.10 ExpansionsinSeries of ${{}_{p}F_{q}}$ Functions
Expansions of the form $\sum_{n=1}^{\infty}(\pm 1)^{n}{{}_{p}F_{p+1}}\left(\mathbf{a};\mathbf{b};-n^{2% }z^{2}\right)$ are discussed in Miller (1997), and further series of generalized hypergeometric functions are given in Luke (1969b, Chapter 9), Luke (1975, §§5.10.2 and 5.11), and Prudnikov et al. (1990, §§5.3, 6.8–6.9).