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1: 26.21 Tables
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►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.
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►Goldberg et al. (1976) contains tables of binomial coefficients to and Stirling numbers to .
2: 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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4.37.19
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3: 19.34 Mutual Inductance of Coaxial Circles
4: 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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5: 12.19 Tables
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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.
6: 4.23 Inverse Trigonometric Functions
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►In (4.23.1) and (4.23.2) the integration paths may not pass through either of the points .
…In (4.23.3) the integration path may not intersect .
… and have branch points at ; the other four functions have branch points at .
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►where and in (4.23.34) and (4.23.35), and in (4.23.36).
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7: 11.8 Analogs to Kelvin Functions
§11.8 Analogs to Kelvin Functions
►For properties of Struve functions of argument see McLachlan and Meyers (1936).8: 4.16 Elementary Properties
9: 28.25 Asymptotic Expansions for Large
10: 4.13 Lambert -Function
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►The decreasing solution can be identified as .
… is a single-valued analytic function on , real-valued when , and has a square root branch point at .
…The other branches are single-valued analytic functions on , have a logarithmic branch point at , and, in the case , have a square root branch point at respectively.
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►and has several advantages over the Lambert -function (see Lawrence et al. (2012)), and the tree -function , which is a solution of
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►where for , for on the relevant branch cuts,
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