gives the logarithm of the Barnes G-function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- LogBarnesG[z] is analytic throughout the complex z plane.
- LogBarnesG[z] is analytic throughout the complex z plane and is defined as .
- For certain special arguments, LogBarnesG automatically evaluates to exact values.
- LogBarnesG can be evaluated to arbitrary numerical precision.
- LogBarnesG automatically threads over lists.
Examplesopen allclose all
Basic Examples (6)
Evaluate at large arguments:
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Series expansion at a singular point:
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 (5)
Values at fixed points:
Value at infinity:
Value at zero:
Find the first positive maximum:
Plot the LogBarnesG 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:
Formula for the derivative with respect to z:
Series Expansions (4)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Find the series expansion at Infinity:
Find series expansion for an arbitrary symbolic direction :
Taylor expansion at a generic point:
Generalizations & Extensions (1)
Properties & Relations (2)