relations%20to%20Lam%C3%A9%20functions
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21: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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§26.4(i) Definitions
… ►It is also the number of -dimensional lattice paths from to . For , the multinomial coefficient is defined to be . … ►(The empty set is considered to have one permutation consisting of no cycles.) … ►§26.4(iii) Recurrence Relation
…22: 6.16 Mathematical Applications
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►Hence, if is fixed and , then , , or according as , , or ; compare (6.2.14).
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►Hence if and , then the limiting value of overshoots by approximately 18%.
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►If we assume Riemann’s hypothesis that all nonreal zeros of have real part of (§25.10(i)), then
…where is the number of primes less than or equal to
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23: 22.16 Related Functions
§22.16 Related Functions
… ►Relation to Elliptic Integrals
… ►Relation to Theta Functions
… ►Relation to the Elliptic Integral
… ►Definition
…24: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Pearson (1965) tabulates the function () for , to 7D, where rounds off to 1 to 7D; also for , to 5D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.