Sentence examples for analytic function of the from inspiring English sources

Since this eigenvalue is an analytic function of the length of the design space, we can make use of a Taylor expansion to provide a recursive algorithm for its calculation.

We prove a noncommutative analogue of the fact that every symmetric analytic function of (z,w) in the bidisc D2 can be expressed as an analytic function of the variables z+w and zw.

The whole surface is presented with explicit formulas, starting from a plane analytic function of the arc length.

The SSDs are expressed as piecewise analytic functions of the scheduled OP.

It will be proved that in this case the support points and weights are real analytic functions of the boundary points of the design space.

The concept of a unitary linear system allows a characterization of the basic Hilbert spaces of analytic functions of the interpolation theory.

We show that the ground state projection and the ground state energy are analytic functions of the coupling constant in a cone with apex at the origin, provided a mild infrared assumption holds.

We show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential, under the assumption that the atomic Hamiltonian has a non-degenerate ground state.

We denote by ℘ the class of analytic functions of the form (1.2) in U.

The analytic functions of the complex variable ( z_{k} = x + mu_{k} y ).

For analytic functions of the form f ( z ) = ∑ n = 1 ∞ a n z n, z ∈ U, (6).