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1: 16.22 Asymptotic Expansions
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►Asymptotic expansions of for large
are given in Luke (1969a, §§5.7 and 5.10) and Luke (1975, §5.9).
For asymptotic expansions of Meijer -functions with large parameters see Fields (1973, 1983).
2: 14.26 Uniform Asymptotic Expansions
§14.26 Uniform Asymptotic Expansions
…3: 34.8 Approximations for Large Parameters
§34.8 Approximations for Large Parameters
►For large values of the parameters in the , , and symbols, different asymptotic forms are obtained depending on which parameters are large. …4: 33.18 Limiting Forms for Large
§33.18 Limiting Forms for Large
…5: 28.16 Asymptotic Expansions for Large
§28.16 Asymptotic Expansions for Large
…6: 12.16 Mathematical Applications
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7: 35.10 Methods of Computation
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►For large
the asymptotic approximations referred to in §35.7(iv) are available.
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►These algorithms are extremely efficient, converge rapidly even for large values of , and have complexity linear in .
8: Bibliography U
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Integrals with a large parameter. Several nearly coincident saddle-points.
Proc. Cambridge Philos. Soc. 72, pp. 49–65.
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Integrals with a large parameter: A double complex integral with four nearly coincident saddle-points.
Math. Proc. Cambridge Philos. Soc. 87 (2), pp. 249–273.
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Integrals with a large parameter: Legendre functions of large degree and fixed order.
Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
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