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ContinuedDiLog

ContinuedDiLog[{x1,α1},{x2,α2}]
gives the two variable Beenakker-Denner continued dilogarithm function .

Details and OptionsDetails and Options

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The function has the contour integral representation
        ,
    where is the contour that starts at on the principal sheet of the complex logarithm and ends at on the Riemann sheet of the logarithm determined by the accumulated phase of the product .
  • If , .
  • ContinuedDiLog[{x1,α1},{x2,α2}] has a branch cut discontinuity in each complex plane running from to .
  • For real negative product , the sign of determines on which side of the branch cut ContinuedDiLog evaluates.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Evaluate numerically:

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Evaluate symbolically:

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Compare the principal value of the dilogarithm function with the analytically continued version:

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