LAUSR

ABSTRACT We introduce an integral transform which may be used to construct new closed-form formulas for series involving alternating harmonic numbers, such as the Ramanujan-like formula introduced in this article which elegantly relates Catalan's constant G with through an infinite summation involving Catalan numbers. Using this integral transform, we also obtain closed-form expressions for new series involving harmonic numbers of even index such as the new summation for Apéry's constant introduced in our article, as well as new proofs of known formulas for series containing harmonic numbers. The techniques introduced in this paper are also used to provide closed-form evaluations for some new definite integrals which state-of-the-art computer algebra systems cannot compute symbolically.