Airy zeta function ~ INDAHNYA BERBAGI

Senin, 09 Juni 2014

Airy zeta function

In mathematics, the Airy zeta function, studied by Crandall (1996), is a function analogous to the Riemann zeta function and related to the zeros of the Airy function.

The Airy function

\mathrm{Ai}(x) = \frac{1}{\pi} \int_0^\infty \cos\left(\tfrac13t^3 + xt\right)\, dt,

is positive for positive x, but oscillates for negative values of x; the sequence of values of x for which Ai(x) = 0, sorted by their absolute values, are called the Airy zeros and are denoted a₁, a₂, ...

The Airy zeta function is the function defined from this sequence of zeros by the series

\zeta_{\mathrm{Ai}}(s)=\sum_{i=1}^{\infty} \frac{1}{|a_i|^s}.

This series converges when the real part of s is greater than 3/2, and may be extended by analytic continuation to other values of s.

Sumber : http://en.wikipedia.org/wiki/Airy_zeta_function

INDAHNYA BERBAGI

Senin, 09 Juni 2014