Sentence examples for continuation of the function from inspiring English sources

Analytic continuation of the function (G x,t,lambda)) with respect to λ out of sectors (S^) and (S^) does not have a singularity on the line (operatorname{Re}(lambdaomega_{0})=0}.

This proves the analytic continuation of the function s ↦ ζ ∗ ( s, α ; x ) as an entire function to the whole complex plane, except simple poles at s = α − n, 0 ≤ n < [ a ] if ℜ ≥ 1.

This proves the analytic continuation of the function s ↦ ζ ( s, α ; x, λ ) as an entire function to the whole complex plane, and Γ E m ( x ; − λ ) = 2 α ζ ( − m, α ; x, λ ).

It is seen that the condition (3.12) guarantees the analytic continuation of the functions (N^) and (N^) from the real axis to the lower and upper half-planes, respectively.

According to the uniqueness theorem of analytic functions, this equality is satisfied for the analytic continuations of the functions on the semi-plane (operatorname{Im} xgeq0) with respect to x, which are on both sides of the given equality.

end{aligned} (40) Note that formula (40) gives an analytic continuation of the matrix function (beta x, lambda)) to the whole λ-plane.

Proponents of this approach believe that it correctly implies, contrary to competing standards, that a human body that is breathing and maintaining circulation is alive regardless of whether continuation of these functions requires external support (as with "brain-dead" patients, locked-in patients, and normal fetuses) (Shewmon 2001; Potts 2001).

In this paper, firstly, we show that by using the Poisson summation formula, the analytic continuation of the Lerch zeta function can be explained and the functional relation for the Lerch zeta function can be obtained in a very elementary way.

The colors help to distinguish the different continuations of the fractal function whose graph is illustrated in black near the center of the image (color figure online).

This finding was considered in the specification of the continuation of caregiving function described below.

These and related policies may help to ensure the continuation of the public health functions of allotment gardens.