Elliptic Functions with Complex Arguments

Coulomb and Bessel Functions of Complex Arguments and Order

The coulomb wavefunctions, originally constructed for real p > 0, real q and integer 2 > 0, are delined for p, n, and 1 all complex. We examine the complex continuation of a variety of series and continued-fraction expansions for the Coulomb functions and their logarithmic derivatives, and then see how these expansions may be selectively combined to calculate both the regular and irregular func...

Trigonometric functions, elliptic functions, elliptic modular forms

Heun functions versus elliptic functions

We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard’s generalization of Floquet’s theory for differential equations with doubly periodic coefficients and give the detailed forms of the level one Heun functions in terms of Jacobi theta functions. The finite-gap solutions give an interesting alternative integr...

Some local fixed point results under $C$-class functions with applications to coupled elliptic systems

The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

Stirling Numbers for Complex Arguments

We define the Stirling numbers for complex values and obtain extensions of certain identities involving these numbers. We also show that the generalization is a natural one for proving unimodality and monotonicity results for these numbers. The definition is based on the Cauchy integral formula and can be used for many other combinatorial numbers.