Manuals/calci/GFUNCTION

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 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})\prod_{k=1}^\infty [{(1+\frac{z}{k})}^k exp(\frac {z^2}{2k}-z)]}

Examples

1. GFUNCTION(10) = 5056584744960000
2. GFUNCTION(4) = 2
3. GFUNCTION(7) = 34560
4. GFUNCTION(5.2) = 12

Related Videos

Gamma Function

See Also

• BETAFUNCTION
• KFUNCTION

References

• G Function

• List of Main Z Functions

• Z3 home