# twelvefold way

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## 1—10 of 89 matching pages

##### 1: 26.17 The Twelvefold Way

###### §26.17 The Twelvefold Way

►The*twelvefold way*gives the number of mappings $f$ from set $N$ of $n$ objects to set $K$ of $k$ objects (putting balls from set $N$ into boxes in set $K$). … ►

##### 2: 31.18 Methods of Computation

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►Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)).
The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.

##### 3: 35.12 Software

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►References to research software that is available in other ways is listed separately.
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##### 4: 5.21 Methods of Computation

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►An effective way of computing $\mathrm{\Gamma}\left(z\right)$ in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion (5.11.3).
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##### 5: 16.9 Zeros

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►Then ${}_{p}{}^{}F_{p}^{}(\mathbf{a};\mathbf{b};z)$ has at most finitely many zeros if and only if the ${a}_{j}$ can be re-indexed for $j=1,\mathrm{\dots},p$ in such a way that ${a}_{j}-{b}_{j}$ is a nonnegative integer.
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##### 6: 16.27 Software

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►References to research software that is available in other ways is listed separately.
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##### 7: 26.22 Software

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►References to research software that is available in other ways is listed separately.
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##### 8: 34.15 Software

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►References to research software that is available in other ways is listed separately.
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##### 9: Jim Pitman

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►He has a continuing interest in the technical management of scientific information in ways that encourage individuals and small organizations to maintain high-quality knowledge repositories that are openly accessible.
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##### 10: Preface

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►The term

*digital library*has gained acceptance for this kind of information resource, and our choice of project title reflects our hope that the NIST DLMF will be a vehicle for revolutionizing the way applicable mathematics in general is practiced and delivered.