A Special Integral Function

A Special Rational Function with Vanishing Integral

The integral of a rational function proposed as a question in Mathematics Stack Exchange is evaluated. The integrand has a polynomial of degree 4 as denominator. A natural extension to degree 8 is shown to vanish.

A Special Case of Selberg’s Integral

We evaluate the integral ∞ 0 · · · ∞ 0 1≤i<j≤n (x j − x i) 2 e −x1 dx 1 · · · e −xn dx n using orthogonal polynomials and techniques from linear algebra.

Special integral variation of trees

In this paper, we determine all trees with the property that adding a particular edge will result in exactly two Laplacian eigenvalues increasing respectively by 1 and the other Laplacian eigenvalues remaining fixed. We also investigate a situation in which the algebraic connectivity is one of the changed eigenvalues.

Integral switching engine for special

Sandwich-type theorems for a class of integral operators with special properties

In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.