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11: 10.17 Asymptotic Expansions for Large Argument
12: 28.25 Asymptotic Expansions for Large
13: 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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14: 22.9 Cyclic Identities
15: 6.4 Analytic Continuation
16: 26.15 Permutations: Matrix Notation
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►where the sum is over
and .
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►Define .
…The rook polynomial is the generating function for :
…
►For , denotes after removal of all elements of the form or , .
denotes with the element removed.
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17: 4.24 Inverse Trigonometric Functions: Further Properties
18: 10.34 Analytic Continuation
19: 26.10 Integer Partitions: Other Restrictions
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►The set is denoted by .
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►where the last right-hand side is the sum over
of the generating functions for partitions into distinct parts with largest part equal to .
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►where the sum is over nonnegative integer values of for which .
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►where the sum is over nonnegative integer values of for which .
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►where the sum is over nonnegative integer values of for which .
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