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21: 7.2 Definitions
22: 7.20 Mathematical Applications
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►For applications of the complementary error function in uniform asymptotic approximations of integrals—saddle point coalescing with a pole or saddle point coalescing with an endpoint—see Wong (1989, Chapter 7), Olver (1997b, Chapter 9), and van der Waerden (1951).
►The complementary error function also plays a ubiquitous role in constructing exponentially-improved asymptotic expansions and providing a smooth interpretation of the Stokes phenomenon; see §§2.11(iii) and 2.11(iv).
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7.20.1
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23: 22.14 Integrals
24: 12.7 Relations to Other Functions
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§12.7(ii) Error Functions, Dawson’s Integral, and Probability Function
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12.7.5
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12.7.6
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12.7.7
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25: 29.18 Mathematical Applications
26: 29.13 Graphics
27: 6.4 Analytic Continuation
28: 29.12 Definitions
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►The superscript on the left-hand sides of (29.12.1)–(29.12.8) agrees with the number of -zeros of each Lamé polynomial in the interval , while is the number of -zeros in the open line segment from to .
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29: 22.13 Derivatives and Differential Equations
30: 6.1 Special Notation
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►The main functions treated in this chapter are the exponential integrals , , and ; the logarithmic integral ; the sine integrals and ; the cosine integrals and .
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