Calculation of generalized elliptic type integrals using the binomial expansion theorem

摘要

Approximate closed form expressions are developed for generalized elliptic type integrals using binomial coefficients. There are utilized to obtain closed form expressions for the Epstein–Hubbell (EH) generalized elliptic-type integral. Numerical test results are also reported. The convergence of series is tested by the concrete cases for values parameters. The formulae obtained are valid for arbitrary parameters’ values.