MellinTransform

MellinTransform[expr,x,s]

gives the Mellin transform of expr.

MellinTransform[expr,{x1,x2,},{s1,s2,}]

gives the multidimensional Mellin transform of expr.

Details and Options

  • The Mellin transform of a function is defined to be .
  • The multidimensional Mellin transform of a function is given by .
  • The Mellin transform of exists only for complex values of such that . In some cases, this strip of definition may extend to a half-plane.
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    GenerateConditionsFalsewhether to generate results that involve conditions on parameters
    MethodAutomaticwhat method to use
  • In TraditionalForm, MellinTransform is output using TemplateBox[{{f, (, x, )}, x, s}, MellinTransform1].

Examples

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Basic Examples  (2)

Compute the Mellin transform of a function:

In[1]:=
Click for copyable input
Out[1]=

Compute a multivariate Mellin transform:

In[1]:=
Click for copyable input
Out[1]=

Scope  (16)

Options  (5)

Applications  (3)

Properties & Relations  (10)

Possible Issues  (1)

Neat Examples  (1)

See Also

InverseMellinTransform  MellinConvolve  LaplaceTransform  FourierTransform  HankelTransform  Integrate  MeijerG  Gamma  MeijerGReduce

Introduced in 2016
(11.0)