In mathematics, a Barnes zeta function is a generalization of the Riemann zeta function introduced by E. W. Barnes (1901). It is further generalized by...

zeta function of a dynamical system Barnes zeta function or double zeta function Beurling zeta function of Beurling generalized primes Dedekind zeta function...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

studied by Takuro Shintani (1976). They include Hurwitz zeta functions and Barnes zeta functions. Let P ( x ) {\displaystyle P(\mathbf {x} )} be a polynomial...

In mathematics, the Hurwitz zeta function is one of the many zeta functions. It is formally defined for complex variables s with Re(s) > 1 and a ≠ 0,...

}{\partial s}}\zeta _{N}(s,w\mid a_{1},\ldots ,a_{N})\right|_{s=0}\right)\ ,} where ζ N {\displaystyle \zeta _{N}} is the Barnes zeta function. (This differs...

quotients of the gamma function, called Mellin–Barnes integrals. An application of the gamma function is the study of the Riemann zeta function. A fundamental...

the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined...

mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function...

tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order 2 – often referred...

Synchrotron function Riemann zeta function: A special case of Dirichlet series. Riemann Xi function Dirichlet eta function: An allied function. Dirichlet...

-\sum _{k=1}^{\infty }(-1)^{k}\,\zeta (k+1)\,z^{k},} which converges for |z| < 1. Here, ζ(n) is the Riemann zeta function. This series is easily derived...

{\bigl [}\zeta '(-1,z)-\zeta '(-1){\bigr ]}} where ζ′(z) denotes the derivative of the Riemann zeta function, ζ(a,z) denotes the Hurwitz zeta function and ζ...

sums and integrals, especially those involving the gamma function and the Riemann zeta function. It is named after mathematicians James Whitbread Lee Glaisher...

} . Evaluations of the digamma function at rational values. The Laurent series expansion for the Riemann zeta function*, where it is the first of the...

Askey–Wilson polynomial, Askey–Wilson function (with James A. Wilson) Ernest William Barnes: Barnes G-function E. T. Bell: Bell polynomials Bender–Dunne...

series expansion of the Riemann zeta function: ζ ( 1 + s ) = 1 s + ∑ n = 0 ∞ ( − 1 ) n n ! γ n s n . {\displaystyle \zeta (1+s)={\frac {1}{s}}+\sum _{n=0}^{\infty...

Yamasaki, Yoshinori (December 2006). "On q-Analogues of the Barnes Multiple Zeta Functions". Tokyo Journal of Mathematics. 29 (2): 413–427. arXiv:math/0412067...

other series for the zeta-function-related cases of the Legendre chi function, the polygamma function, and the Riemann zeta function include χ 1 ( z ) =...

Riemann zeta function ζ ( s ) ∼ ∑ n = 1 N n − s + N 1 − s s − 1 − N − s 2 + N − s ∑ m = 1 ∞ B 2 m s 2 m − 1 ¯ ( 2 m ) ! N 2 m − 1 {\displaystyle \zeta (s)\sim...

x+\sum _{k=2}^{\infty }{\frac {\,\zeta (k)\,}{k}}\,(-x)^{k}} where ζ ( k ) {\textstyle \zeta (k)} is the Riemann zeta function. Then applying Ramanujan master...

produce one of the fundamental formulas for the Riemann zeta function, ζ ( s ) {\displaystyle \zeta (s)} . Let f ( x ) = 1 e x − 1 {\textstyle f(x)={\frac...

definition Hardy–Littlewood inequality Hardy–Littlewood maximal function Hardy–Littlewood zeta function conjectures Hardy–Littlewood tauberian theorem First Hardy–Littlewood...

include number theory, zeta theory, and mathematical analysis. He is mostly recognized for the Matsumoto zeta function, a zeta function named after him. He...

mathematical constants Mathematical constant Particular values of Riemann zeta function Papanikolaou, Thomas (March 1997). Catalan's Constant to 1,500,000 Places...

Nations Messenger of Peace in 1998. He has been married to actress Catherine Zeta-Jones since 2000. Douglas was born in New Brunswick, New Jersey, the first...

Ono, Ken (2003), "A q-series identity and the arithmetic of Hurwitz zeta functions", Proceedings of the American Mathematical Society, 131 (3): 719–724...

Riemann zeta function, and this method[clarification needed] is still used to relate the modular transformation law of the Jacobi theta function to the...

group of the ring of integers of a number field to the field's Dedekind zeta function. Bombieri–Lang conjectures on densities of rational points of algebraic...

campus. The fraternity is Sigma Tau Gamma and the sororities are Delta Zeta and Zeta Tau Alpha. The co-education service fraternity is Alpha Phi Omega. There...