recursion relations

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21: 25.6 Integer Arguments

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§25.6(i) Function Values

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§25.6(iii) Recursion Formulas

… ►For related results see Basu and Apostol (2000).

22: 27.14 Unrestricted Partitions

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§27.14(ii) Generating Functions and Recursions

… ►Multiplying the power series for $f\left(x\right)$ with that for $1/f\left(x\right)$ and equating coefficients, we obtain the recursion formula …Logarithmic differentiation of the generating function $1/f\left(x\right)$ leads to another recursion: … ►These recursions can be used to calculate $p\left(n\right)$, which grows very rapidly. … ►This is related to the function $f\left(x\right)$ in (27.14.2) by …

23: 8.18 Asymptotic Expansions of $I_x(a,b)$

… ►A recurrence relation for the $d_k$ can be found in Nemes and Olde Daalhuis (2016). …