Catalan%20constant
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11: 30.9 Asymptotic Approximations and Expansions
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βΊ
§30.9(i) Prolate Spheroidal Wave Functions
βΊAs , with , … βΊThe asymptotic behavior of and as in descending powers of is derived in Meixner (1944). …The asymptotic behavior of and as is given in Erdélyi et al. (1955, p. 151). The behavior of for complex and large is investigated in Hunter and Guerrieri (1982). …12: 8 Incomplete Gamma and Related
Functions
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13: 28 Mathieu Functions and Hill’s Equation
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14: 23 Weierstrass Elliptic and Modular
Functions
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15: 36.5 Stokes Sets
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βΊwhere denotes a real critical point (36.4.1) or (36.4.2), and denotes a critical point with complex or , connected with by a steepest-descent path (that is, a path where ) in complex or space.
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βΊ
36.5.4
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βΊ
36.5.7
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βΊ
βΊ
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16: 11.6 Asymptotic Expansions
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βΊ
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11.6.1
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βΊwhere is an arbitrary small positive constant.
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βΊ
11.6.2
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βΊwhere is Euler’s constant (§5.2(ii)).
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βΊ
17: 5.11 Asymptotic Expansions
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βΊThe scaled gamma function is defined in (5.11.3) and its main property is as in the sector .
Wrench (1968) gives exact values of up to .
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βΊIn this subsection , , and are real or complex constants.
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βΊ
5.11.12
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βΊ
5.11.19
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18: 25.6 Integer Arguments
19: 15.10 Hypergeometric Differential Equation
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βΊThe connection formulas for the principal branches of Kummer’s solutions are:
βΊ
15.10.17
βΊ
15.10.18
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βΊ
15.10.21
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βΊ
15.10.25
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20: 36 Integrals with Coalescing Saddles
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