analytic continuation

Noun

Meaning

(mathematical analysis) The practice of extending analytic functions.

(mathematical analysis) An extension of an analytic function which is itself analytic.

Examples

Hasse's conjecture affirms that the L-function admits an analytic continuation to the whole complex plane and satisfies a functional equation relating, for any s, L(E, s) to L(E, 2 − s). Source: Internet

Instead of the above ad hoc analytic continuation assumption, non-convergent sums and integrals are computed using Euler–Maclaurin summation with a regularizing function (e. Source: Internet

The formula also holds for all α ≠ −n, −n − 1, … by analytic continuation, but then the function and its Fourier transforms need to be understood as suitably regularized tempered distributions. Source: Internet

The functional equation was established by Riemann in his 1859 paper On the Number of Primes Less Than a Given Magnitude and used to construct the analytic continuation in the first place. Source: Internet

Close letter words and terms