Examples of using Zeta function in English and their translations into Turkish
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The Riemann zeta function.
Hurwitz's zeta function occurs in a variety of disciplines.
Motivic Igusa zeta functions.
Nontrivial zeros, zeta functions and a lot of other stuff that goes totally over my head.
Here, ζ is the Riemann zeta function.
The Riemann zeta function is ζ"s", 1.
And here you see something that is basically the Riemann zeta function appearing.
The zeta function occurs in applied statistics see Zipf's law and Zipf-Mandelbrot law.
This intimately relates them to the values of the zeta function at negative integers.
In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions. .
Note that this latter form is the functional equation for the Riemann zeta function, as originally given by Riemann.
We see that the zeroes of the Riemann Zeta function… correspond to singularities… in space-time… Singularities in space-time then… After?
It's a mathematical conjecture from the 19th century that states that the Riemann zeta function zeroes all lie on the critical line.
Infinite series===The zeta function evaluated at positive integers appears in infinite series representations of a number of constants.
Singularities in space-time then… So,we see that the zeroes of the Riemann Zeta function… correspond to singularities… in space-time.
These upper bounds have since been reduced considerably by using largescale computer calculations of zeros of the Riemann zeta function.
So, we see that the zeroes of the Riemann Zeta function correspond to singularities in space-time.
The zeta function has become a vital element in our present understanding of the distribution of the building blocks of all numbers, the primes.
The most usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions.
The Riemann zeta function also appears in a form similar to the Mellin transform in an integral over the Gauss-Kuzmin-Wirsing operator acting on"x""s"-1; that context gives rise to a series expansion in terms of the falling factorial.
We see that the zeroes of the Riemann Zeta function… After? Welcome! in space-time… correspond to singularities.
Scorer's function Sinc function Hermite polynomialsLaguerre polynomials Chebyshev polynomials Riemann zeta function: A special case of Dirichlet series.
Dirichlet L-function* Hurwitz zeta function* Legendre chi function* Lerch transcendent* Polylogarithm and related functions:** Incomplete polylogarithm** Clausen function** Complete Fermi-Dirac integral, an alternate form of the polylogarithm.
All lie on the critical line. that states that the Riemann Zeta function zeroes It's a mathematical conjecture from the 19th century.
Euler treated these two as special cases of for arbitrary"n", a line of research extending his work onthe Basel problem and leading towards the functional equations of what are now known as the Dirichlet eta function and the Riemann zeta function.
Fourier transform==The discrete Fourier transform of the Hurwitz zeta function with respect to the order"s" is the Legendre chi function. .
If X is a zeta-distributed random variable with parameter s, then the probability that X takes the integer value k is given by the probability mass function f s( k) k- s/ ζ( s){\displaystyle f_{ s}( k)= k^{- s}/\ zeta(s)\,} where ζ(s)is the Riemann zeta function which is undefined for s 1.
However, if 0<q<1 and q≠1/2,then there are zeros of Hurwitz's zeta function in the strip 1<Re(s)<1+ε for any positive real number ε.
Zeros==If"q"=1 the Hurwitz zeta function reduces to the Riemann zeta function itself; if"q"=1/2 it reduces to the Riemann zeta function multiplied by a simple function of the complex argument"s"("vide supra"), leading in each case to the difficult study of the zeros of Riemann's zeta function. .
Scorer's function* Sinc function* Hermite polynomials* Chebyshev polynomials===Riemann zeta andrelated functions===* Riemann zeta function: A special case of Dirichlet series.