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1: 4.42 Solution of Triangles
2: 5.21 Methods of Computation
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►An effective way of computing in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion (5.11.3).
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3: About the Project
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4: 25.19 Tables
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5: 32.15 Orthogonal Polynomials
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►For this result and applications see Fokas et al. (1991): in this reference, on the right-hand side of Eq.
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6: 16.5 Integral Representations and Integrals
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►In the case the left-hand side of (16.5.1) is an entire function, and the right-hand side supplies an integral representation valid when .
In the case the right-hand side of (16.5.1) supplies the analytic continuation of the left-hand side from the open unit disk to the sector ; compare §16.2(iii).
Lastly, when the right-hand side of (16.5.1) can be regarded as the definition of the (customarily undefined) left-hand side.
In this event, the formal power-series expansion of the left-hand side (obtained from (16.2.1)) is the asymptotic expansion of the right-hand side as in the sector , where is an arbitrary small positive constant.
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7: 22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
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8: 2.3 Integrals of a Real Variable
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►assume and are finite, and is infinitely differentiable on .
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►When is real and is a large positive parameter, the main contribution to the integral
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2.3.13
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►When the parameter is large the contributions from the real and imaginary parts of the integrand in
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2.3.19
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9: 2.4 Contour Integrals
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►Let denote the path for the contour integral
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2.4.10
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2.4.14
►and apply the result of §2.4(iii) to each integral on the right-hand side, the role of the series (2.4.11) being played by the Taylor series of and at .
…Thus the right-hand side of (2.4.14) reduces to the error terms.
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10: 19.32 Conformal Map onto a Rectangle
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►As proceeds along the entire real axis with the upper half-plane on the right, describes the rectangle in the clockwise direction; hence is negative imaginary.
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