power-series expansions
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11—20 of 57 matching pages
11: 19.19 Taylor and Related Series
§19.19 Taylor and Related Series
… ►12: 7.17 Inverse Error Functions
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§7.17(ii) Power Series
…13: 19.5 Maclaurin and Related Expansions
14: 8.7 Series Expansions
§8.7 Series Expansions
…15: 28.6 Expansions for Small
16: 11.13 Methods of Computation
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►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 , they are cumbersome to use when is large owing to slowness of convergence and cancellation.
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17: 30.4 Functions of the First Kind
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§30.4(iii) Power-Series Expansion
…18: 11.2 Definitions
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§11.2(i) Power-Series Expansions
…19: 12.15 Generalized Parabolic Cylinder Functions
20: 10.74 Methods of Computation
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►The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument or is sufficiently small in absolute value.
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►In the interval , needs to be integrated in the forward direction and in the backward direction, with initial values for the former obtained from the power-series expansion (10.2.2) and for the latter from asymptotic expansions (§§10.17(i) and 10.20(i)).
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