gives the Barnes G-function .
- BarnesG is also known as the double gamma function.
- Mathematical function, suitable for both symbolic and numeric manipulation.
- The Barnes G-function is defined as for positive integers and is otherwise defined as .
- The Barnes G-function satisfies the functional equation .
- BarnesG[z] is an entire function of z with no branch cut discontinuities.
- For certain special arguments, BarnesG automatically evaluates to exact values.
- BarnesG can be evaluated to arbitrary numerical precision.
- BarnesG automatically threads over lists.
- BarnesG can be used with Interval and CenteredInterval objects. »
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (5)
Specific Values (4)
Plot the BarnesG function:
Function Properties (10)
BarnesG is defined for all real and complex values:
Approximate function range of BarnesG:
BarnesG is an analytic function of x:
BarnesG is neither non-increasing nor non-decreasing:
BarnesG is not injective:
BarnesG is surjective:
BarnesG is neither non-negative nor non-positive:
BarnesG has no singularities or discontinuities:
BarnesG is neither convex nor concave:
BarnesG may be generated by symbolic solvers:
The determinant of this Cauchy matrix can be expressed in terms of BarnesG. Verify with a specific value of for the first few cases:
Properties & Relations (2)
Wolfram Research (2008), BarnesG, Wolfram Language function, https://reference.wolfram.com/language/ref/BarnesG.html (updated 2022).
Wolfram Language. 2008. "BarnesG." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/BarnesG.html.
Wolfram Language. (2008). BarnesG. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BarnesG.html