Integration Formulas Involving Fibonacci and Lucas Numbers

Abstract

We present a range of dicult integration formulas involving Fi-bonacci and Lucas numbers and trigonometric functions. These formulas are often expressed in terms of special functions like the dilogarithm and Clausen'sfunction. We also prove complements of integral identities of Dilcher (2000) and Stewart (2022). Many of our results are based on a fundamental lemma dealing with di erentiation of complex-valued Fibonacci (Lucas) functions.