Zeta (UK: /ˈziːtə/, US: /ˈzeɪtə/; uppercase Ζ, lowercase ζ; Ancient Greek: ζῆτα, Demotic Greek: ζήτα, classical [d͡zɛ̌ːta] or [zdɛ̌ːta] zē̂ta; Greek pronunciation:...

function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined as ζ ( s ) = ∑ n = 1 ∞ 1 n s = 1 1 s + 1 2 s...

values of which are ζ ′ ( − 2 ) = − ζ ( 3 ) 4 π 2 ζ ′ ( − 4 ) = 3 4 π 4 ζ ( 5 ) ζ ′ ( − 6 ) = − 45 8 π 6 ζ ( 7 ) ζ ′ ( − 8 ) = 315 4 π 8 ζ ( 9 ) . {\displaystyle...

the reciprocals of the positive cubes. That is, it is defined as the number ζ ( 3 ) = ∑ n = 1 ∞ 1 n 3 = lim n → ∞ ( 1 1 3 + 1 2 3 + ⋯ + 1 n 3 ) , {\displaystyle...

ζ-Carotene (zeta-carotene) is a carotenoid. It is different from α-carotene and β-carotene because it is acyclic. ζ-Carotene is similar in structure to...

parameter, denoted by ζ ("zeta"), that can vary from undamped (ζ = 0), underdamped (ζ < 1) through critically damped (ζ = 1) to overdamped (ζ > 1). The behaviour...

zeta, ZETA, Zeta, zéta, or zêta in Wiktionary, the free dictionary. Zeta (Ζ or ζ) is the sixth letter of the Greek alphabet. Zeta or ZETA may also refer...

− ζ τ ( c 1 e τ ζ 2 − 1 + c 2 e − τ ζ 2 − 1 ) ζ > 1  (overdamping) e − ζ τ ( c 1 + c 2 τ ) = e − τ ( c 1 + c 2 τ ) ζ = 1  (critical damping) e − ζ τ [...

( 2 ) H n ( 4 ) + 2 H n ( 6 ) ) → n → ∞ 1 6 π 6 ( ζ ( 2 ) 3 − 3 ζ ( 2 ) ζ ( 4 ) + 2 ζ ( 6 ) ) ⟹ ζ ( 6 ) = π 6 945 = − 3 ⋅ π 6 [ x 6 ] sin ⁡ ( x ) x −...

constellation of Orion. It has the designations ζ Orionis, which is Latinised to Zeta Orionis and abbreviated Zeta Ori or ζ Ori, and 50 Orionis, abbreviated 50 Ori...

the undamped angular frequency of the oscillator or the natural frequency, ζ = c 2 m k {\displaystyle \zeta ={\frac {c}{2{\sqrt {mk}}}}} is called the...

Riemann hypothesis for curves over finite fields. The Riemann zeta function ζ(s) is a function whose argument s may be any complex number other than 1,...

Lorentz boost (x direction with rapidity ζ) c t ′ = c t cosh ⁡ ζ − x sinh ⁡ ζ x ′ = x cosh ⁡ ζ − c t sinh ⁡ ζ y ′ = y z ′ = z {\displaystyle {\begin{aligned}ct'&=ct\cosh...

ζ. These are overdamped (ζ > 1), underdamped (ζ < 1), and critically damped (ζ = 1). The overdamped response (ζ > 1) is I ( t ) = A 1 e − ω 0 ( ζ + ζ...

form: x ¨ + 2 ζ ω n x ˙ + ω n 2 x = u {\displaystyle {\ddot {x}}+2\zeta \omega _{n}{\dot {x}}+\omega _{n}^{2}x=u} where ω n = k m ; ζ = c 2 m ω n ; u...

z = ζ + 1 ζ , {\displaystyle z=\zeta +{\frac {1}{\zeta }},} where z = x + i y {\displaystyle z=x+iy} is a complex variable in the new space and ζ = χ...

,z)} is A ϕ = μ 0 I π R l [ ζ ( R + ρ ) 2 + ζ 2 ( m + n − m n m n K ( m ) − 1 m E ( m ) + n − 1 n Π ( n , m ) ) ] ζ − ζ + , {\displaystyle A_{\phi }={\frac...

(}\,{\overline {\zeta }}\,{\big )}=0} as well. If P(ζ  ) = 0, then a 0 + a 1 ζ + a 2 ζ 2 + ⋯ + a n ζ n = 0 {\displaystyle a_{0}+a_{1}\zeta +a_{2}\zeta ^{2}+\cdots...

Zeta Ophiuchi (ζ Oph, ζ Ophiuchi) is a single star located in the constellation of Ophiuchus. It has an apparent visual magnitude of 2.6, making it the...

-\varepsilon _{\rm {C}}.} We can define a parameter ζ that references the Fermi level with respect to the band edge: ζ = μ − ϵ C . {\displaystyle \zeta =\mu -\epsilon...

Catherine Zeta-Jones (/ˈziːtə/; born 25 September 1969) is a Welsh actress. Recognised for her versatility, she has received various accolades, including...

we have | ζ | n ≤ ‖ a ‖ p ( | ζ | q ( n − 1 ) + ⋯ + | ζ | q + 1 ) 1 q = ‖ a ‖ p ( | ζ | q n − 1 | ζ | q − 1 ) 1 q ≤ ‖ a ‖ p ( | ζ | q n | ζ | q − 1 )...

ζ ) {\displaystyle S(\zeta )} is the squeeze operator, given by D ^ ( α ) = exp ⁡ ( α a ^ † − α ∗ a ^ ) and S ^ ( ζ ) = exp ⁡ [ 1 2 ( ζ ∗ a ^ 2 − ζ a...

identities: ζ ( s ) = 1 − s + 2 − s + 3 − s + 4 − s + 5 − s + 6 − s + ⋯ 2 × 2 − s ζ ( s ) = 2 × 2 − s + 2 × 4 − s + 2 × 6 − s + ⋯ ( 1 − 2 1 − s ) ζ ( s ) =...

r = ( cos ⁡ θ cos ⁡ ζ cos ⁡ θ sin ⁡ ζ sin ⁡ θ ) e θ = ( − sin ⁡ θ cos ⁡ ζ − sin ⁡ θ sin ⁡ ζ cos ⁡ θ ) e ζ = ( − sin ⁡ ζ cos ⁡ ζ 0 ) {\displaystyle \mathbf...

result in number theory that states the Apéry's constant ζ(3) is irrational. That is, the number ζ ( 3 ) = ∑ n = 1 ∞ 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 + ⋯ =...

Zeta Reticuli, Latinized from ζ Reticuli, is a wide binary star system in the southern constellation of Reticulum. From the southern hemisphere the pair...

formally defined for complex variables s with Re(s) > 1 and a ≠ 0, −1, −2, … by ζ ( s , a ) = ∑ n = 0 ∞ 1 ( n + a ) s . {\displaystyle \zeta (s,a)=\sum _{n=0}^{\infty...

transformation f can be written [ ζ ,   1 ] ( a c b d )   =   [ a ζ + b ,   c ζ + d ]   =   [ a ζ + b c ζ + d ,   1 ]   =   [ f ( ζ ) ,   1 ] . {\displaystyle...

Naos, also known by its Bayer designation of Zeta Puppis (ζ Puppis, abbreviated Zeta Pup or ζ Pup), is the brightest star in the constellation of Puppis...