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11—20 of 512 matching pages
11: 26.18 Counting Techniques
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: 4.16 Elementary Properties
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βΊ
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14: 10.17 Asymptotic Expansions for Large Argument
15: 28.25 Asymptotic Expansions for Large
16: 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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17: 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
… βΊ18: 6.4 Analytic Continuation
19: 26.15 Permutations: Matrix Notation
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βΊwhere the sum is over
and .
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βΊDefine .
…The rook polynomial is the generating function for :
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βΊFor , denotes after removal of all elements of the form or , .
denotes with the element removed.
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20: 19.16 Definitions
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βΊIn (19.16.1)–(19.16.2_5), except that one or more of may be 0 when the corresponding integral converges.
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βΊ