Numerical indefinite integration of functions with singularities

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for H-P functions, for p > 1, over the interval (-1, 1). The main factor i n the error of our indefinite quadrature formula is O(e(-pi rootN/q)), with 2N nodes and 1/p + 1/q = 1 The convergence rate of our formula is better t han that of the Stenger-type formulas by a factor of root2 in the constant of the exponential. We conjecture that our formula has the best possible va lue for that constant. The results of numerical examples show that our inde finite quadrature formula is better than Haber's indefinite quadrature form ula for H-P-Functions.