2020/02/08 by Md Sarowar Morshed, Morshed, Md Sarowar
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2002.03250
openalex publication_date 2020/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The need to evaluate Logarithmic integrals is ubiquitous in essentially all\nquantitative areas including mathematical sciences, physical sciences. Some\nrecent developments in Physics namely Feynman diagrams deals with the\nevaluation of complicated integrals involving logarithmic functions. This work\ndeals with a systematic review of logarithmic integrals starting from Malmsten\nintegrals to classical collection of Integrals, Series and Products by I. S.\nGradshteyn and I. M. Ryzhik [1] to recent times. The evaluation of these types\nof integrals involves higher transcendental functions (i.e., Hurwitz Zeta\nfunction, Polylogarithms, Lerch Transcendental, Orthogonal Polynomials,\nPolyGamma functions). In a more general sense the following types of integrals\nare considered for this work: n
int0a f(x)
ln
g(x)
dx with a \∈ R+ , f(x)\nand g(x) both either rational/trigonometric or both type of functions.\n