Legendre chi function

The Legendre chi function (after Adrien -Marie Legendre ) is a special function in mathematics.

Definition

The Legendre chi function is defined as follows:

They can also be expressed with the Polylogarithmus:

With the imaginary unit and the catalanschen constants.

The special cases include the Dirichlet lambda function

And the Dirichlet beta function:

The transcendent lerchsche zeta function generalizes the Legendre chi function:

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