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 .
- BarnesG can be evaluated to arbitrary numerical precision.
- BarnesG automatically threads over lists.
Examplesopen allclose all
Basic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
Specific Values (4)
Value at infinity:
Value at zero:
Evaluate symbolically at half‐integer orders:
Find the first positive maximum:
Plot the BarnesG function:
Plot the real part of :
Plot the imaginary part of :
First derivatives with respect to z:
Higher derivatives with respect to z:
Plot the higher derivatives with respect to z:
Series Expansions (3)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Find the series expansion at Infinity:
Taylor expansion at a generic point:
Properties & Relations (2)
Neat Examples (1)
Determinants of Hankel matrices built out of Bell numbers: