Abstract
A method to derive a convergent series suitable for numerical computation of a family of special functions of complex variable defined in the form of a definite integral is proposed. A variable transformation is applied by which singular points of the special function are mapped on or outside the circle of convergence of the power series of the new variable. Using this method, multivalued functions can be evaluated even outside the principal sheet of the Riemann surface. As a typical example, an application of the method to the exponential integral is investigated.
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