涉及斐波那契和卢卡斯数的积分公式

arXiv - MATH - General Mathematics Pub Date : 2024-05-30 DOI:arxiv-2406.00064

Kunle Adegoke, Robert Frontczak

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引用次数: 0

摘要

我们提出了一系列涉及斐波那契数、卢卡斯数和三角函数的困难积分公式。这些公式通常用稀释算术和克劳森函数等特殊函数表示。我们还证明了 Dilcher (2000) 和 Stewart (2022) 的积分等式的补全。我们的许多结果都是基于处理复值斐波那契（卢卡斯）函数微分的基本定理。

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Integration Formulas Involving Fibonacci and Lucas Numbers

We present a range of difficult integration formulas involving Fibonacci and Lucas numbers and trigonometric functions. These formulas are often expressed in terms of special functions like the dilogarithm and Clausen's function. 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 differentiation of complex-valued Fibonacci (Lucas) functions.

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arXiv - MATH - General Mathematics

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