# 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).
##### 5: 18.40 Methods of Computation
However, for applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev. …
##### 7: 8.7 Series Expansions
###### §8.7 SeriesExpansions
8.7.6 $\Gamma\left(a,x\right)=x^{a}e^{-x}\sum_{n=0}^{\infty}\frac{L^{(a)}_{n}\left(x% \right)}{n+1},$ $x>0$.
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).
##### 8: 28.11 Expansions in Series of Mathieu Functions
###### §28.11 ExpansionsinSeries of Mathieu Functions
28.11.7 $\sin(2m+2)z=\sum_{n=0}^{\infty}B_{2m+2}^{2n+2}(q)\mathrm{se}_{2n+2}\left(z,q% \right).$