Gauss's multiplication formula.
Updated 6 Jan 2011

View License

In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various relations all stem from the same underlying principle; that is, the relation for one special function can be derived from that for the others, and is simply a manifestation of the same identity in different guises.

The multiplication theorem is:

G(a)*G(a+1/b)*G(a+2/b)*...*G(a + b-1/b) = prod_[k=0 to b-1] G(a + k/b)

= (2*pi)^(b/2)*b^(1/2-ab)*G(ab)

where G is the gamma function.

For integer k >= 1, and is sometimes called Gauss's multiplication formula, in honour of Carl Friedrich Gauss.

Cite As

Antonio Trujillo-Ortiz (2024). gaussmult (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R14
Compatible with any release
Platform Compatibility
Windows macOS Linux
Find more on Numerical Integration and Differential Equations in Help Center and MATLAB Answers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes

It was added an appropriate format to cite this file.