conjugate%20Poisson%20integral
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11: 10.75 Tables
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Achenbach (1986) tabulates , , , , , 20D or 18–20S.
Zhang and Jin (1996, p. 270) tabulates , , , , , 8D.
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.
Zhang and Jin (1996, p. 322) tabulates , , , , , , , , , 7S.
12: 1.15 Summability Methods
13: 1.8 Fourier Series
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1.8.6_1
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1.8.6_2
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►(1.8.10) continues to apply if either or or both are infinite and/or has finitely many singularities in , provided that the integral converges uniformly (§1.5(iv)) at , and the singularities for all sufficiently large .
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§1.8(iv) Poisson’s Summation Formula
… ►It follows from definition (1.14.1) that the integral in (1.8.14) is equal to . …14: 18.33 Polynomials Orthogonal on the Unit Circle
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18.33.1
►where the bar signifies complex conjugate.
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►where the bar again signifies complex conjugate.
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►where the bar signifies complex conjugate and , .
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►for , while .
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15: 26.9 Integer Partitions: Restricted Number and Part Size
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►The conjugate partition is obtained by reflecting the Ferrers graph across the main diagonal or, equivalently, by representing each integer by a column of dots.
The conjugate to the example in Figure 26.9.1 is .
Conjugation establishes a one-to-one correspondence between partitions of into at most parts and partitions of into parts with largest part less than or equal to .
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16: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
§8.26(iv) Generalized Exponential Integral
►Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
17: 36.8 Convergent Series Expansions
§36.8 Convergent Series Expansions
… ►For multinomial power series for , see Connor and Curtis (1982). ►
36.8.3
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36.8.4
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36.8.5
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18: 36 Integrals with Coalescing Saddles
Chapter 36 Integrals with Coalescing Saddles
…19: 12.10 Uniform Asymptotic Expansions for Large Parameter
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►Here bars do not denote complex conjugates; instead
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12.10.26
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12.10.27
►and the function has the asymptotic expansion
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12.10.30
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