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:
Special values
With the imaginary unit and the catalanschen constants.
Special cases and generalizations
The special cases include the Dirichlet lambda function
And the Dirichlet beta function:
The transcendent lerchsche zeta function generalizes the Legendre chi function: