# Laurent series

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## 9 matching pages

##### 5: 1.10 Functions of a Complex Variable
###### §1.10(iii) LaurentSeries
This singularity is removable if $a_{n}=0$ for all $n<0$, and in this case the Laurent series becomes the Taylor series. … The coefficient $a_{-1}$ of $(z-z_{0})^{-1}$ in the Laurent series for $f(z)$ is called the residue of $f(z)$ at $z_{0}$, and denoted by $\Residue_{z=z_{0}}[f(z)]$, $\Residue\limits_{z=z_{0}}[f(z)]$, or (when there is no ambiguity) $\Residue[f(z)]$. …
##### 6: 25.2 Definition and Expansions
25.2.4 $\zeta\left(s\right)=\frac{1}{s-1}+\sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!}\gamma% _{n}(s-1)^{n},$
##### 7: 2.10 Sums and Sequences
2.10.25 $f(z)=\sum_{n=-\infty}^{\infty}f_{n}z^{n},$ $0<|z|.
##### 8: Bibliography H
• P. I. Hadži (1976a) Expansions for the probability function in series of Čebyšev polynomials and Bessel functions. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
• G. H. Hardy (1912) Note on Dr. Vacca’s series for $\gamma$ . Quart. J. Math. 43, pp. 215–216.
• G. H. Hardy (1949) Divergent Series. Clarendon Press, Oxford.
• E. Hendriksen and H. van Rossum (1986) Orthogonal Laurent polynomials. Nederl. Akad. Wetensch. Indag. Math. 48 (1), pp. 17–36.
• E. Hille (1929) Note on some hypergeometric series of higher order. J. London Math. Soc. 4, pp. 50–54.
• ##### 9: Bibliography V
• H. Van de Vel (1969) On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.
• J. F. Van Diejen and V. P. Spiridonov (2001) Modular hypergeometric residue sums of elliptic Selberg integrals. Lett. Math. Phys. 58 (3), pp. 223–238.
• R. S. Varma (1941) An infinite series of Weber’s parabolic cylinder functions. Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
• A. N. Vavreck and W. Thompson (1984) Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.
• H. Volkmer (2021) Fourier series representation of Ferrers function ${\sf P}$ .