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power-series expansion


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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. …
2: 12.4 Power-Series Expansions
§12.4 Power-Series Expansions
3: 14.32 Methods of Computation
In particular, for small or moderate values of the parameters μ and ν the power-series expansions of the various hypergeometric function representations given in §§14.3(i)14.3(iii), 14.19(ii), and 14.20(i) can be selected in such a way that convergence is stable, and reasonably rapid, especially when the argument of the functions is real. …
4: 16.25 Methods of Computation
Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. …
5: 33.19 Power-Series Expansions in r
§33.19 Power-Series Expansions in r
6: 33.6 Power-Series Expansions in ρ
§33.6 Power-Series Expansions in ρ
7: 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. … Thus the regular solutions can be computed from the power-series expansions (§§33.6, 33.19) for small values of the radii and then integrated in the direction of increasing values of the radii. … Noble (2004) obtains double-precision accuracy for W η , μ ( 2 ρ ) for a wide range of parameters using a combination of recurrence techniques, power-series expansions, and numerical quadrature; compare (33.2.7). …
8: 28.15 Expansions for Small q
§28.15(i) Eigenvalues λ ν ( q )
9: 7.6 Series Expansions
§7.6(i) Power Series
10: 30.3 Eigenvalues
§30.3(iv) Power-Series Expansion