1rgamma1

1rgamma1 is a shorthand that appears in a minority of mathematical and software documentation. It is not a standard mathematical object with a single canonical definition, so the precise meaning depends on the context.

One common interpretation is that it denotes the reciprocal gamma function evaluated at a particular argument, written as 1/Γ(z). In this view, 1rgamma1 would mean the value at z = 1, which is 1 because Γ(1) = 1. More generally, the reciprocal gamma function 1/Γ(z) is an entire function with simple zeros at z = 0, -1, -2, ... and is used in certain integral representations and series expansions.

In other contexts, 1rgamma1 may be used informally as a label for a programming routine or a site-specific notation for a one-parameter gamma-related function. It should not be confused with the gamma function Γ(z) itself or with R's rgamma function, which in the statistical software generates gamma-distributed random variates.

Relation to distributions: If someone uses a gamma-related family, there exists the inverse gamma distribution; however that is a separate concept from the reciprocal gamma function.

See also: Gamma function, Reciprocal gamma function, Inverse gamma distribution, R rgamma.