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The plots above show the values of the function obtained by taking the natural logarithm of the gamma function, lnGamma(z). Note that this introduces complicated branch cut ...

A method for testing nested hypotheses. To apply the procedure, given a specific model, calculate the likelihood of observing the actual data. Then compare this likelihood to ...

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 ...

The log sine function, also called the logsine function, is defined by S_n=int_0^pi[ln(sinx)]^ndx. (1) The first few cases are given by S_1 = -piln2 (2) S_2 = ...

The logarithm log_bx for a base b and a number x is defined to be the inverse function of taking b to the power x, i.e., b^x. Therefore, for any x and b, x=log_b(b^x), (1) or ...

For all integers n and |x|<a, lambda_n^((t))(x+a)=sum_(k=0)^infty|_n; k]lambda_(n-k)^((t))(a)x^k, where lambda_n^((t)) is the harmonic logarithm and |_n; k] is a Roman ...

A branch point whose neighborhood of values wrap around an infinite number of times as their complex arguments are varied. The point z=0 under the function lnz is therefore a ...

The logarithmic capacity of a compact set E in the complex plane is given by gamma(E)=e^(-V(E)), (1) where V(E)=inf_(nu)int_(E×E)ln1/(|u-v|)dnu(u)dnu(v), (2) and nu runs over ...

The logarithmic derivative of a function f is defined as the derivative of the logarithm of a function. For example, the digamma function is defined as the logarithmic ...

The logarithmic distribution is a continuous distribution for a variate X in [a,b] with probability function P(x)=(lnx)/(b(lnb-1)-a(lna-1)) (1) and distribution function ...