This chapter focuses on the indefinite integrals of logarithmic functions. Various combinations of logarithms and polynomials are reviewed. Integrands involving combinations of ln( ax ) and powers of x are discussed that include integrands involving x m ln n (ax) , integrands involving ln m (ax)...
02 A quantum integral connecting the gamma and zeta functions【连接伽马函数和泽塔函数的量子积分】 07:37 Integral of x^2sin(x) from zero to pi2 13:20 An awesome hyperbolic gaussian boi integral of e^(-x^2)cosh(x) from zero to 09:27 An elegant 2nd order non-linear differential equation...
Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums We show that integrals of the form and satisfy certain recurrence relations which allow us to write them in terms of Euler sums. From this we prove that, i... P Freitas - 《Math Comp》 被引量: 54发表:...
Indefinite integral of a linear combination of functions If and are two functions and are two constants, then In other words, the integral of a linear combination is equal to the linear combinations of the integrals. This property is called "linearity of the integral". Two special cases of th...
Module 2: Applications of Integration Search for: Introduction to Integrals, Exponential Functions, and LogarithmsWhat you’ll learn to do: Apply integration and derivatives to exponential and natural logarithmic functions We already examined exponential functions and logarithms in earlier chapters. Howeve...
Integration of Exponential and Logarithmic Functions: Methods and formulas to integrate functions like e^x, ln(x), etc. Integration of Hyperbolic Functions: Techniques for integrating functions like sinh(x), cosh(x), etc. Linearity of the Integral: The principle that the integral of a sum is ...
The goal of this series of article is to present a systematic treatment of so called "polylogarithmic integral", they and their related objects are frequently discussed among integral/series enthusiasts. A typical example is ∫01logaxlogb(1−x)logc(1+x)xdx . Before the introductio...
By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple z... C Xu - 《Mathematica Slovaca》 被引量: 11发表: 2017年 Mu...
Adamchik, V.: A class of logarithmic integrals. In: Proceedings ISSAC, pp. 1–8 (1997) Apelblat, A.: Tables of Integrals and Series. Verlag Harry Deutsch, Thun, Frankfurt am Main (1996) Baxter, R.J., Temperley, H.N.V., Ashley, S.E.: Triangular Potts model at its transition...
We'll ignore that final complex function offor now, and continue with the evaluation of the complex logarithmic integral part: We already have the closed form for the two leftmost CL-type integrals, so it remains to find the remaining two SL-types. [The real logcosine moments are omitted ...