Manuals/calci/GFUNCTION

GFUNCTION (Number)

• $Number$ is any positive real number.

Description

• This function shows the value of the Barnes G-function value.
• In $GFUNCTION(Number)$,$Number$ is any real number.
• $G(z)$ 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:

$G(1+z)={(2\pi )}^{\frac {z}{2}}exp(-{\frac {z+z^{2}(1+\gamma )}{2}})\prod _{k=1}^{\infty }[{(1+{\frac {z}{k}})}^{k}exp({\frac {z^{2}}{2k}}-z)]$

Examples

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

See Also

• BETAFUNCTION
• KFUNCTION

References

• G Function

• List of Main Z Functions

• Z3 home