Q-gamma function

In q-analog theory, the -gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related to the double gamma function. It was introduced by . It is given by when , and if . Here is the infinite q-Pochhammer symbol. The -gamma function satisfies the functional equation In addition, the -gamma function satisfies the q-analog of the Bohr–Mollerup theorem, which was found by Richard Askey .For non-negative integers n, The relation to the ordinary gamma function is made explicit in the limit

Q-gamma function

In q-analog theory, the -gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related to the double gamma function. It was introduced by . It is given by when , and if . Here is the infinite q-Pochhammer symbol. The -gamma function satisfies the functional equation In addition, the -gamma function satisfies the q-analog of the Bohr–Mollerup theorem, which was found by Richard Askey .For non-negative integers n, The relation to the ordinary gamma function is made explicit in the limit