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A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

The gamma product (e.g., Prudnikov et al. 1986, pp. 22 and 792), is defined by Gamma[a_1,...,a_m; b_1,...,b_n]=(Gamma(a_1)...Gamma(a_m))/(Gamma(b_1)...Gamma(b_n)), where ...

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

The log-series distribution, also sometimes called the logarithmic distribution (although this work reserves that term for a distinct distribution), is the distribution of ...

A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times ...

The integral representation of ln[Gamma(z)] by lnGamma(z) = int_1^zpsi_0(z^')dz^' (1) = int_0^infty[(z-1)-(1-e^(-(z-1)t))/(1-e^(-t))](e^(-t))/tdt, (2) where lnGamma(z) is the ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

gamma_r=(kappa_r)/(sigma^(r+2)), where kappa_r are cumulants and sigma is the standard deviation.

The exponential sum function e_n(x), sometimes also denoted exp_n(x), is defined by e_n(x) = sum_(k=0)^(n)(x^k)/(k!) (1) = (e^xGamma(n+1,x))/(Gamma(n+1)), (2) where ...

where Gamma(z) is the gamma function and other details are discussed by Gradshteyn and Ryzhik (2000).