论文标题
评估Malmsten的积分和相关积分的新方法
A new approach to evaluating Malmsten's integral and related integrals
论文作者
论文摘要
本文讨论了对数和双曲线积分的概括。发现了Vardi提出的积分和其他几个积分与已知数学常数有关的新证明。我们从第一类的广义stirling多项式中介绍了第一类签名的普遍多项式，并根据Stirling Cypering循环数量和完整的Bell多项式为签名的第一种符号广义的Stirling多项式提供了新的表达式。我们确定了第一类签名的广义多项式的作用，并在概括了Malmsten的所有自然力量的积分中，为双曲线脱位函数的所有自然力量不可或缺，并且我们得出了积分序列的还原公式。我们给出了新的积分序列的表达式，该序列具有与Malmsten的积分相似的特性，该序列就第一类的签名的广义stirling多项式而言，我们发现了第一类签名的广义stirling多项式的身份和功能方程。
This paper discusses generalizations of logarithmic and hyperbolic integrals. A new proof for an integral presented by Vardi and several other integrals in relation to known mathematical constants are discovered. We introduce the signed generalized Stirling polynomials of the first kind from the generalized Stirling polynomials of the first kind, and we give new expressions for the signed generalized Stirling polynomials of the first kind in terms of the Stirling cycle numbers and complete Bell polynomials. We establish the role of the signed generalized Stirling polynomials of the first kind and complete Bell polynomials in generalizing Malmsten's integral for all natural powers of the hyperbolic secant function, and we derive a reduction formula for the integral sequence. We give expressions for new integral sequences, which possess similar properties with Malmsten's integral, in terms of the signed generalized Stirling polynomials of the first kind, and we discover identities and a functional equation for the signed generalized Stirling polynomials of the first kind.
