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11: 26.18 Counting Techniques
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βΊThen the number of elements in the set is
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26.18.1
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βΊNote that this is also one of the counting problems for which a formula is given in Table 26.17.1.
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12: 11.8 Analogs to Kelvin Functions
§11.8 Analogs to Kelvin Functions
βΊFor properties of Struve functions of argument see McLachlan and Meyers (1936).13: 10.25 Definitions
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βΊThis equation is obtained from Bessel’s equation (10.2.1) on replacing by , and it has the same kinds of singularities.
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βΊIn particular, the principal branch of is defined in a similar way: it corresponds to the principal value of , is analytic in , and two-valued and discontinuous on the cut .
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βΊThe principal branch corresponds to the principal value of the square root in (10.25.3), is analytic in , and two-valued and discontinuous on the cut .
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βΊTable 10.25.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.25.1).
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βΊ
14: 28.25 Asymptotic Expansions for Large
15: 4.13 Lambert -Function
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βΊThe 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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βΊand 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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βΊwhere for , for on the relevant branch cuts,
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16: 22.9 Cyclic Identities
§22.9 Cyclic Identities
… βΊ§22.9(ii) Typical Identities of Rank 2
… βΊ βΊ§22.9(iii) Typical Identities of Rank 3
… βΊ17: 7.23 Tables
§7.23 Tables
… βΊThis section lists relevant tables that appeared later. … βΊZhang and Jin (1996, pp. 637, 639) includes , , , 8D; , , , 8D.
Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of , , , 7D and 8D, respectively; the real and imaginary parts of , , , 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.
Fettis et al. (1973) gives the first 100 zeros of and (the table on page 406 of this reference is for , not for ), 11S.
18: Charles W. Clark
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βΊHe has been a Visiting Fellow at the Australian National University, a Dr.
Lee Fellow at Christ Church College of the University of Oxford, and Visiting Professor at the National University of Singapore.
βΊClark received the R&D 100 Award, Distinguished Presidential Rank Award of the U.
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