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large variable and/or large parameter

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1: 12.11 Zeros
§12.11(iii) Asymptotic Expansions for Large Parameter
2: 8.20 Asymptotic Expansions of E p ( z )
§8.20(ii) Large p
3: 16.11 Asymptotic Expansions
§16.11(iii) Expansions for Large Parameters
16.11.10 F p p + 1 ( a 1 + r , , a k - 1 + r , a k , , a p + 1 b 1 + r , , b k + r , b k + 1 , , b p ; z ) = n = 0 m - 1 ( a 1 + r ) n ( a k - 1 + r ) n ( a k ) n ( a p + 1 ) n ( b 1 + r ) n ( b k + r ) n ( b k + 1 ) n ( b p ) n z n n ! + O ( 1 r m ) ,
4: 34.8 Approximations for Large Parameters
§34.8 Approximations for Large Parameters
For large values of the parameters in the 3 j , 6 j , and 9 j symbols, different asymptotic forms are obtained depending on which parameters are large. …
5: 8.12 Uniform Asymptotic Expansions for Large Parameter
§8.12 Uniform Asymptotic Expansions for Large Parameter
Inverse Function
6: 13.8 Asymptotic Approximations for Large Parameters
§13.8 Asymptotic Approximations for Large Parameters
§13.8(i) Large | b | , Fixed a and z
§13.8(ii) Large b and z , Fixed a and b / z
§13.8(iii) Large a
7: 8.11 Asymptotic Approximations and Expansions
§8.11 Asymptotic Approximations and Expansions
8: 12.14 The Function W ( a , x )
§12.14(ix) Uniform Asymptotic Expansions for Large Parameter
Positive a , 2 a < x <
Airy-type Uniform Expansions
9: 8.18 Asymptotic Expansions of I x ( a , b )
§8.18(i) Large Parameters, Fixed x
§8.18(ii) Large Parameters: Uniform Asymptotic Expansions
Symmetric Case
General Case
Inverse Function
10: Bibliography F
  • S. Farid Khwaja and A. B. Olde Daalhuis (2014) Uniform asymptotic expansions for hypergeometric functions with large parameters IV. Anal. Appl. (Singap.) 12 (6), pp. 667–710.
  • J. L. Fields (1973) Uniform asymptotic expansions of certain classes of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.
  • J. L. Fields (1983) Uniform asymptotic expansions of a class of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.