A Note On Nielsen-Type Integrals, Logarithmic Integrals And Higher Harmonic Sums

Abstract

Due to the great success of hypergeometric functions, we provide the analytical solutions of certain definite logarithmic integrals and Nielsen-type integrals in terms of multi-variable Kamp´e de F´eriet functions with suitable convergence conditions and higher harmonic sums by using series rearrangement technique and incomplete Gamma function. Further we also obtain the solution of other related logarithmic integrals in terms of generalized hypergeometric functions and Kummer’s confluent hypergeometric functions by using series rearrangement technique. The results presented in the paper and comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica.