Difference between revisions of "Manuals/calci/GFUNCTION"
Jump to navigation
Jump to search
(Created page with "<div style="font-size:30px">'''GFUNCTION (Number)'''</div><br/> *<math>Number</math> is any positive real number. ==Description== *This function shows the value of the Barne...") |
|||
| Line 9: | Line 9: | ||
*According to elementary factors, it is a special case of the double gamma function. | *According to elementary factors, it is a special case of the double gamma function. | ||
*Formally, the Barnes G-function is defined in the following Weierstrass product form: | *Formally, the Barnes G-function is defined in the following Weierstrass product form: | ||
| − | <math>G(1+z)={(2\pi)}^\frac{z}{2}</math> | + | <math>G(1+z)={(2\pi)}^\frac{z}{2}exp(-\frac{z+z^2(1+\gamma)}{2})</math> |
Revision as of 14:54, 8 August 2017
GFUNCTION (Number)
- is any positive real number.
is any positive real number.Description
- This function shows the value of the Barnes G-function value.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle GFUNCTION (Number)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is any real number.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G(z)} is a function that is an extension of super factorials to the complex numbers.
- It is related to the Gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes.
- According to elementary factors, it is a special case of the double gamma function.
- Formally, the Barnes G-function is defined in the following Weierstrass product form:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G(1+z)={(2\pi)}^\frac{z}{2}exp(-\frac{z+z^2(1+\gamma)}{2})}