Ad
related to: sigma vs zeta
Search results
Results From The WOW.Com Content Network
The Riemann zeta function ζ(s) is a function of a complex variable s = σ + it, where σ and t are real numbers. (The notation s, σ, and t is used traditionally in the study of the zeta function, following Riemann.) When Re (s) = σ > 1, the function can be written as a converging summation or as an integral: where. is the gamma function.
t. e. Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
The letter sigma, in standard orthography, has two variants: ς, used only at the ends of words, and σ, used elsewhere. The form ϲ ("lunate sigma", resembling a Latin c) is a medieval stylistic variant that can be used in both environments without the final/non-final distinction.
Riemann hypothesis. This plot of Riemann's zeta (ζ) function (here with argument z) shows trivial zeros where ζ (z) = 0, a pole where ζ (z) = , the critical line of nontrivial zeros with Re (z) = 1/2 and slopes of absolute values. In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at ...
Weierstrass functions. Mathematical functions related to Weierstrass's elliptic function. In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for Karl Weierstrass. The relation between the sigma, zeta, and functions is analogous to that ...
Divisor function σ 0 (n) up to n = 250 Sigma function σ 1 (n) up to n = 250 Sum of the squares of divisors, σ 2 (n), up to n = 250 Sum of cubes of divisors, σ 3 (n) up to n = 250. In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.
Zeta (UK: / ˈziːtə /, US: / ˈzeɪtə /; [1] uppercase Ζ, lowercase ζ; Ancient Greek: ζῆτα, Demotic Greek: ζήτα, classical [d͡zɛ̌ːta] or [zdɛ̌ːta] zē̂ta; Greek pronunciation: [ˈzita] zíta) is the sixth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 7. It was derived from the Phoenician ...
The damping ratio is a parameter, usually denoted by ζ (Greek letter zeta), [7] that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator. In general, systems with higher damping ratios (one or greater ...