analytic continuation in a sentence
1) Euler summation is essentially an explicit form of analytic continuation .
analytic collocations
2) Other methods involve analytic continuations of related series.
3) Several summation methods involve taking the value of an analytic continuation of a function.
analytic continuation example sentences
4) Analytic continuation of G(z), its poles and residues.5) Examples of regular functions defined by series or integrals and their analytic continuations .
6) Uniqueness of analytic continuations and applications.
7) Such a function, and its analytic continuations , is called the hypergeometric function.
8) It introduces multivalued functions, analytic continuation and integral transforms, especially Fourier and Laplace transforms.
9) This process of extending the original branch Log by gluing compatible holomorphic functions is known as analytic continuation .
10) The universal cover first arose in the theory of analytic functions as the natural domain of an analytic continuation .
11) A further generalization is to replace the sum under the integral by its analytic continuation from small "t".
12) Systematic treatment of such factorization, and of the analytic continuation , will be taken up later. 1.
13) For the other arguments with Re("z") 1⁄2 the result follows by analytic continuation .
14) Integral representations can be important for theoretical reasons, e.g. giving analytic continuation or functional equations, or sometimes for numerical evaluations.
15) The first origins of sheaf theory are hard to pin down - they may be co-extensive with the idea of analytic continuation .
example sentences with analytic continuation
16) In many cases, a Dirichlet series can be extended to an analytic function outside the domain of convergence by analytic continuation .17) Often this means that this function is a certain L-function and this gives an analytic continuation and functional equation for this L-function.
18) Analytic continuation :.
19) From a theorem in complex analysis , there is a unique analytic continuation of this real function to the domain of complex numbers.
20) Analytic continuation of the solution "Y" around any pole λ"i" and back to the basepoint will produce a new solution "Y'".
21) The identity __FORMULA__ continues to hold when both functions are extended by analytic continuation to include values of "s" for which the above series diverge.
22) The benefit of introducing the Riemann zeta function is that it can be defined for other values of "s" by analytic continuation .
23) Bernhard Riemann further contributed to their theory, clarifying the geometric meaning of the process of analytic continuation of functions of complex variables.
24) Euler used it before analytic continuation was defined in general, and gave explicit formulas for the power series of the analytic continuation.
25) Euler used it before analytic continuation was defined in general, and gave explicit formulas for the power series of the analytic continuation .
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