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1: 12.19 Tables
§12.19 Tables
►Abramowitz and Stegun (1964, Chapter 19) includes and for , , 5S; for , , 4-5D or 4-5S.
Kireyeva and Karpov (1961) includes for , , and , , 7D.
Karpov and Čistova (1964) includes for , ; , , 6D.
Zhang and Jin (1996, pp. 455–473) includes , , , , and derivatives, , , , 8S; , , and derivatives, , and , , , 8S. Also, first zeros of , , and of derivatives, , 6D; first three zeros of and of derivative, , 6D; first three zeros of and of derivative, , 6D; real and imaginary parts of , , , , , 8S.
2: 4.16 Elementary Properties
3: 36.7 Zeros
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►The zeros in Table 36.7.1 are points in the plane, where is undetermined.
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Table 36.7.1: Zeros of cusp diffraction catastrophe to 5D.
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, .
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Zeros inside, and zeros outside, the cusp . | |||||
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4: 26.21 Tables
§26.21 Tables
►Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients for up to 50 and up to 25; extends Table 26.4.1 to ; tabulates Stirling numbers of the first and second kinds, and , for up to 25 and up to ; tabulates partitions and partitions into distinct parts for up to 500. ►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts , partitions into parts , and unrestricted plane partitions up to 100. It also contains a table of Gaussian polynomials up to . ►Goldberg et al. (1976) contains tables of binomial coefficients to and Stirling numbers to .5: 4.37 Inverse Hyperbolic Functions
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►In (4.37.1) the integration path may not pass through either of the points , and the function assumes its principal value when is real.
In (4.37.2) the integration path may not pass through either of the points , and the function assumes its principal value when .
…In (4.37.3) the integration path may not intersect .
… and have branch points at ; the other four functions have branch points at .
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►Table 4.30.1 can also be used to find interrelations between inverse hyperbolic functions.
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6: 4.21 Identities
§4.21 Identities
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4.21.1
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4.21.4
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4.21.5
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►In (4.21.21)–(4.21.23) Table 4.16.1 and analytic continuation will assist in resolving sign ambiguities.
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7: 19.34 Mutual Inductance of Coaxial Circles
8: 19.22 Quadratic Transformations
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19.22.5
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19.22.19
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►However, if and are complex conjugates and and are real, then the right-hand sides of all transformations in §§19.22(i) and 19.22(iii)—except (19.22.3) and (19.22.22)—are free of complex numbers and .
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