A bstract We show that the differential equation for three-loop equal-mass banana integral can be cast into an ? -factorised form with entries constructed from (meromorphic) modular forms and one special function, which given as iterated of meromorphic forms. The allows a systematic solution to any order in dimensional regularisation parameter . alphabet integrals contains six letters.

By using the second main theorem of the meromorphic function on annuli, we investigate the problem on two meromorphic functions partially sharing five or more values and obtain some theorems that improve and generalize the previous results given by Cao and Yi.

In the present paper certain subclasses of strongly starlike and strongly convex functions defined by convolution with the generalized Hurwitz -Lerch Zeta function are investigated. Some inclusion relations are also mentioned as special cases of our main results.

AbstractIn this paper we introduce the subclass K(μ, γ, η, α, β) of β-uniformly convex and β-uniformly starlike functions which are analytic and multivalent with negative coefficients defined by using fractional calculus operators. Characterization property exhibited by the functions in the class and the results of modified Hadamard product are discussed. Connections with the popular subclasses...

Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randić indices for matching, whose values depend on the structure of the tree. We also find the expression of these indices for starlike tree and a double-starlike tree, Hm(p, q). Moreover, we show that two cospectral Hm(p, q) of the same ...

The main concerned target of this article is to define and study some classes meromorphic function spaces using the general spherical derivatives. Besov-type functions as well normal are considered intensively both compared deeply with each other. Specifically, multiple results concerning meromorphic-type non-normal obtained by help proved constructing specific mild conditions on sequences poin...

It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...

We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is CP1 and the function is a polynomial, we give an elementary way of finding this number. In the general case, we show that, as the multiplicities of critical points tend to infinity, the asymptotic for the number of ...