arXiv Open Access 2023

Values and recurrence relations for integrals of powers of arctan and logarithm and associated Euler-like sums

Xiaoyu Liu Xinhua Xiong

Lihat Sumber

Abstrak

In this paper, we give evaluations of integrals involving the arctan and the logarithm functions, and present several new summation identities for odd harmonic numbers and Milgram constants. These summation identities can be expressed as finite sums of special constants such as $π$, the Catalan constant, the values of Riemann zeta function at the positive odd numbers and $\ln2$ etc.. Some examples are detailed to illustrate the theorems.

Topik & Kata Kunci

math.NT

Penulis (2)

Xiaoyu Liu

Xinhua Xiong

Format Sitasi

APA MLA BibTeX

Liu, X., Xiong, X. (2023). Values and recurrence relations for integrals of powers of arctan and logarithm and associated Euler-like sums. https://arxiv.org/abs/2308.01583

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓