Subordination Involving Regular Coulomb Wave Functions

Some Relationships Involving Subordination

If X(t) is a stochastic process taking values in some space 9C and g is a real-valued function on 9C then we may consider the process g(X(t)). Often from some knowledge about the process X(t) and the function g one can deduce properties of the process g(X(t)). For example: if X(t) is Brownian motion in R" and g is a subharmonic function on Rn that doesn't grow too fast then g(X(t)) is a semimar...

Calculation of the matrix elements of the Coulomb interaction involving relativistic hydrogenic wave functions

A program is presented for calculation of the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψ † f (r)|R − r|−1ψi(r)dr . Bound-free transitions are considered. Relativistic hydrogenic wave functions are used for the numerical evaluation of the matrix elements. The applied algorithm is based on the multipole series expansion of the Coulomb potenti...

Subclasses of Bi-Univalent Functions of Complex Order Based On Subordination Conditions Involving Wright Hypergeometric Functions

In this paper, we introduce and investigate a new subclass of biunivalent functions ∑ of complex order defined in the open unit disk, which are associated with hypergeometric functions and satisfy subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients 2 | | a and 3 | | a for functions in the new subclass. Several (known or new) consequences of the results ar...

Subordination by convex functions

Subordination by Convex Functions

Let K(α), 0≤α< 1, denote the class of functions g(z)= z+∑∞n=2anzn which are regular and univalently convex of order α in the unit disc U . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U , f(0) = 0, and f(z)+zf ′(z) < g(z)+zg′(z) in U , then (i) f(z) < g(z) at least in |z| < r0, r0 = √ 5/3 = 0.745 . . . if f ∈ K; and (ii) f...