digamma function


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digamma function

[′dī‚gam·ə ‚fəŋk·shən]
(mathematics)
The derivative of the natural logarithm of the gamma function.
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where B(a, b) = [GAMMA](a) [GAMMA] (b)/ [GAMMA] (a + b) and [PSI](x)is the digamma function, the asymptotic expression of SOP at high MER can be written as
Merkle, Convexity, Schur-convexity and bounds for the gamma function involving the digamma function, Rocky Mountain J.
Then we establish some sharp inequalities for the digamma function xp, that is the logarithmic derivative of the gamma function,
where [psi](x) is the digamma function, [psi] (k, x) is the kth polygamma function, and M ~ ln(n) + [gamma] + 1/2n + O (1/[n.
as well, where [PSI](n, x) is the nth polygamma function, which is the nth derivative of the digamma function, [PSI](x) := (ln([GAMMA](x)))'= [GAMMA]'(x)/[GAMMA](x).
where [Mathematical Expression Omitted], n = effective population size, v = the single-locus mutation rate, and [Psi] ([center dot]) is the digamma function (Nei 1987, pp.
where [phi]* = 2 ln [GAMMA]*/dx is the digamma function as defined in [21],
t]]dt is the kth-order digamma function which is also called the polygamma function.
is the Eider's constant), which is known in literature as psi or digamma function.
The psi or digamma function [psi](x) = [GAMMA]'(x)/[GAMMA](x), the logarithmic derivative of the gamma function, and the polygamma functions can be expressed for x > 0 and k = 1, 2, .
The psi or digamma function, the logarithmic derivative of the gamma function and the polygamma functions can be expressed as
Zubair, "Extended gamma and digamma functions," Fractional Calculus & Applied Analysis, vol.