×

zbMATH — the first resource for mathematics

On some generalization of Frullani and Dirichlet formulas. (Ukrainian) Zbl 0924.26002
The authors give formulas for the calculation of the following integrals depending on parameters: \(I_{u}(\alpha,\beta)=\int_{a}^{b}[f(\alpha u(x))-f(\beta u(x))]/v(x)dx\) and \(D_{u}(\beta)=\int\limits_{a}^{b}\sin(\beta u(x))/v(x)dx\), where \(f\) is a continuous function; \(u\) is a monotonic continuously-differentiable function; \(u(a)=0, \lim_{x\to b}u(x)=+\infty, v(x)u'(x)=\gamma u(x), \gamma=\text{const}\).
MSC:
26A06 One-variable calculus
26A48 Monotonic functions, generalizations
PDF BibTeX XML Cite