Built-in Mathematica Symbol

MeijerG

MeijerG[{{a₁, ..., a_n}, {a_n+1, ..., a_p}}, {{b₁, ..., b_m}, {b_m+1, ..., b_q}}, z]
is the Meijer G function

.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

The generalized form MeijerG[alist, blist, z, r] is defined for real r by , where in the default case .

In many special cases, MeijerG is automatically converted to other functions.

EXAMPLES

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Basic Examples (2)

Many special functions are special cases of MeijerG:

Evaluate numerically:

Many special functions are special cases of MeijerG:

Evaluate numerically:

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Out[1]=

Scope (8)

Evaluate for complex arguments and parameters:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

MeijerG threads element-wise over lists in the last argument:

Series expansion:

Series expansion in a logarithmic case:

Series expansion at infinity:

TraditionalForm formatting:

Generalizations & Extensions (1)

Evaluate a generalized Meijer G function:

The analogous ordinary Meijer G function has a different branch cut structure:

Applications (2)

Solve a differential equation:

MeijerG gives a logarithmic part:

Integrate can return answers involving MeijerG:

Properties & Relations (1)

Use FunctionExpand to expand MeijerG into simpler functions:

Possible Issues (3)

For some choices of parameters MeijerG is not defined:

is a singular point of MeijerG functions with

:

MeijerG is a piecewise analytic function for

:

Neat Examples (2)

Solve a SIAM 100-digit challenge problem: find

to maximize:

Plot the integral:

Numerically find the maximum:

Generate many elementary and special functions as special cases of MeijerG: