large κ
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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: 27.16 Cryptography
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►Applications to cryptography rely on the disparity in computer time required to find large primes and to factor large integers.
►For example, a code maker chooses two large primes and of about 400 decimal digits each.
…For this reason, the codes are considered unbreakable, at least with the current state of knowledge on factoring large numbers.
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6: 28.16 Asymptotic Expansions for Large
§28.16 Asymptotic Expansions for Large
…7: 12.16 Mathematical Applications
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8: 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 .
9: 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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