A number of families of elliptic-type integrals have been studied recently due to their importance and potential for applications in some problems of radiation physics. The object of this work is to present a unified and generalized form of such elliptic-type integrals and to study its properties, including recurrence formulas and asymptotic expansion.

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

We use AdS/CFT inspired methods to study the Lorentz group SO(1, d + 1) Racah coefficients for type I representations. For such representations the Racah coefficient can be represented as an integral of a product of 6 bulk-to-bulk propagators over 4 copies of the hyperbolic space Hd+1. To compute the integrals we represent the bulk-to-bulk propagators in terms of bulk-to-boundary ones. The bulk...

Introducing a higher order modulus of smoothness based on qintegers, in this paper first we obtain Jackson-type estimates in approximation by Jackson-type generalizations of the q-Picard and q-Gauss-Weierstrass singular integrals and give their global smoothness preservation property with respect to the uniform norm. Then, we study approximation and geometric properties of the complex variants ...

In this article we present a high-precision evaluation of the expansions in ǫ = (4−d)/2 of (up to) fourloop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of ‘QED-type’ master integrals, i.e. those with a single mass scale only (i.e. mi ∈ {0,m}) and an even number of massive lines at each vertex. Furthermore, we collec...