large variable
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21—30 of 109 matching pages
21: 10.72 Mathematical Applications
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►where is a real or complex variable and is a large real or complex parameter.
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►In regions in which (10.72.1) has a simple turning point , that is, and are analytic (or with weaker conditions if is a real variable) and is a simple zero of , asymptotic expansions of the solutions for large
can be constructed in terms of Airy functions or equivalently Bessel functions or modified Bessel functions of order (§9.6(i)).
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►Then for large
asymptotic approximations of the solutions can be constructed in terms of Bessel functions, or modified Bessel functions, of variable order (in fact the order depends on and ).
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22: 33.21 Asymptotic Approximations for Large
23: 33.5 Limiting Forms for Small , Small , or Large
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§33.5(iv) Large
…24: 10.41 Asymptotic Expansions for Large Order
25: Bibliography L
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The solutions of the Mathieu equation with a complex variable and at least one parameter large.
Trans. Amer. Math. Soc. 36 (3), pp. 637–695.
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A Numerical Library in C for Scientists and Engineers.
CRC Press, Boca Raton, FL.
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A Numerical Library in Java for Scientists & Engineers.
Chapman & Hall/CRC, Boca Raton, FL.
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26: 2.8 Differential Equations with a Parameter
27: 10.20 Uniform Asymptotic Expansions for Large Order
28: 8.18 Asymptotic Expansions of
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§8.18(i) Large Parameters, Fixed
… ►§8.18(ii) Large Parameters: Uniform Asymptotic Expansions
►Large , Fixed
… ►Symmetric Case
… ►General Case
…29: 12.10 Uniform Asymptotic Expansions for Large Parameter
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►In this section we give asymptotic expansions of PCFs for large values of the parameter that are uniform with respect to the variable
, when both and
are real.
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30: 4.45 Methods of Computation
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§4.45(i) Real Variables
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4.45.1
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►Another method, when is large, is to sum
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