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1: 24.4 Basic Properties
§24.4(iv) Finite Expansions
2: 27.10 Periodic Number-Theoretic Functions
is a periodic function of n ( mod k ) and has the finite Fourier-series expansionThe finite Fourier expansion of a primitive Dirichlet character χ ( mod k ) has the form …
3: 33.6 Power-Series Expansions in ρ
§33.6 Power-Series Expansions in ρ
The series (33.6.1), (33.6.2), and (33.6.5) converge for all finite values of ρ . Corresponding expansions for H ± ( η , ρ ) can be obtained by combining (33.6.5) with (33.4.3) or (33.4.4).
4: Bibliography C
  • L. Comtet (1974) Advanced Combinatorics: The Art of Finite and Infinite Expansions. enlarged edition, D. Reidel Publishing Co., Dordrecht.
  • 5: 11.13 Methods of Computation
    Although the power-series expansions (11.2.1) and (11.2.2), and the Bessel-function expansions of §11.4(iv) converge for all finite values of z , they are cumbersome to use when | z | is large owing to slowness of convergence and cancellation. …
    6: 13.29 Methods of Computation
    Although the Maclaurin series expansion (13.2.2) converges for all finite values of z , it is cumbersome to use when | z | is large owing to slowness of convergence and cancellation. …
    7: 33.19 Power-Series Expansions in r
    The expansions (33.19.1) and (33.19.3) converge for all finite values of r , except r = 0 in the case of (33.19.3).
    8: 33.23 Methods of Computation
    The power-series expansions of §§33.6 and 33.19 converge for all finite values of the radii ρ and r , respectively, and may be used to compute the regular and irregular solutions. …
    9: 9.17 Methods of Computation
    Although the Maclaurin-series expansions of §§9.4 and 9.12(vi) converge for all finite values of z , they are cumbersome to use when | z | is large owing to slowness of convergence and cancellation. …
    10: 8.25 Methods of Computation
    Although the series expansions in §§8.7, 8.19(iv), and 8.21(vi) converge for all finite values of z , they are cumbersome to use when | z | is large owing to slowness of convergence and cancellation. …