small x
(0.004 seconds)
11—20 of 102 matching pages
11: 8.7 Series Expansions
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►For an expansion for in series of Bessel functions that converges rapidly when and () is small or moderate in magnitude see Barakat (1961).
12: 14.1 Special Notation
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►The main functions treated in this chapter are the Legendre functions , , , ; Ferrers functions , (also known as the Legendre functions on the cut); associated Legendre functions , , ; conical functions , , , , (also known as Mehler functions).
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►Among other notations commonly used in the literature Erdélyi et al. (1953a) and Olver (1997b) denote and by and , respectively.
Magnus et al. (1966) denotes , , , and by , , , and , respectively.
Hobson (1931) denotes both and by ; similarly for and .
, , | real variables. |
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arbitrary small positive constant. | |
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13: 2.5 Mellin Transform Methods
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►The sum in (2.5.6) is taken over all poles of in the strip , and it provides the asymptotic expansion of for small values of .
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2.5.43
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14: 6.18 Methods of Computation
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►For small or moderate values of and , the expansion in power series (§6.6) or in series of spherical Bessel functions (§6.10(ii)) can be used.
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15: 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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16: 18.25 Wilson Class: Definitions
17: 3.2 Linear Algebra
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►The sensitivity of the solution vector in (3.2.1) to small perturbations in the matrix and the vector is measured by the condition number
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18: 19.36 Methods of Computation
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►Similarly, §19.26(ii) eases the computation of functions such as when () is small compared with .
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19: 36.12 Uniform Approximation of Integrals
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►For example, the diffraction catastrophe defined by (36.2.10), and corresponding to the Pearcey integral (36.2.14), can be approximated by the Airy function when is large, provided that and are not small.
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