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Laurent series

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1: 4.33 Maclaurin Series and Laurent Series
§4.33 Maclaurin Series and Laurent Series
2: 4.19 Maclaurin Series and Laurent Series
§4.19 Maclaurin Series and Laurent Series
3: 23.17 Elementary Properties
§23.17(ii) Power and Laurent Series
4: 23.9 Laurent and Other Power Series
§23.9 Laurent and Other Power Series
5: 1.10 Functions of a Complex Variable
§1.10(iii) Laurent Series
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 res z = z 0 [ f ( z ) ] , res z = z 0 [ f ( z ) ] , or (when there is no ambiguity) res [ f ( z ) ] . …
6: 25.2 Definition and Expansions
25.2.4 ζ ( s ) = 1 s - 1 + n = 0 ( - 1 ) n n ! γ n ( s - 1 ) n ,
7: 2.10 Sums and Sequences
2.10.25 f ( z ) = n = - f n z n , 0 < | z | < r .
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 γ . 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.
  • N. Ja. Vilenkin and A. U. Klimyk (1991) Representation of Lie Groups and Special Functions. Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms. Mathematics and its Applications (Soviet Series), Vol. 72, Kluwer Academic Publishers Group, Dordrecht.