poles H ( z ) = ( 1 − q 1 z − 1 ) ( 1 − q 2 z − 1 ) ⋯ ( 1 − q M z − 1 ) ( 1 − p 1 z − 1 ) ( 1 − p 2 z − 1 ) ⋯ ( 1 − p N z − 1 ) , {\displaystyle H(z)={\frac...

Z-Library (abbreviated as z-lib, formerly BookFinder) is a shadow library project for file-sharing access to scholarly journal articles, academic texts...

( z ) = e − 1 2 + 0 − z + 1 z − 1 2 + 2 − z + 2 z − 2 2 + 4 − z + 3 z − 3 2 + 6 − z + 4 z − 4 2 + 8 − z + 5 z − 5 2 + 10 − z + ⋱ +   e − 1 z + 0 − z +...

Z + {\displaystyle \mathbb {Z} _{+}} or Z > {\displaystyle \mathbb {Z} ^{>}} for the positive integers, Z 0 + {\displaystyle \mathbb {Z} ^{0+}} or Z ≥...

{B} (z_{1},z_{2})\,\Gamma (z_{1}+z_{2}).} We have ∂ ∂ z 1 B ( z 1 , z 2 ) = B ( z 1 , z 2 ) ( Γ ′ ( z 1 ) Γ ( z 1 ) − Γ ′ ( z 1 + z 2 ) Γ ( z 1 + z 2 )...

ln(1 + z) when z is small, |z| < 1, since then ln ⁡ ( 1 + z ) = z − z 2 2 + z 3 3 − ⋯ ≈ z . {\displaystyle \ln(1+z)=z-{\frac {z^{2}}{2}}+{\frac {z^{3}}{3}}-\cdots...

value of z {\displaystyle z} , or z ′ {\displaystyle z'} , is defined by: z ′ = 2 ⋅ z − near far − near − 1 {\displaystyle z'=2\cdot {\frac {{z}-{\textit...

= b 0 + b 1 z − 1 + b 2 z − 2 1 + a 1 z − 1 + a 2 z − 2 {\displaystyle \ H(z)={\frac {b_{0}+b_{1}z^{-1}+b_{2}z^{-2}}{1+a_{1}z^{-1}+a_{2}z^{-2}}}} High-order...

function f ( z ) ≜ z 2 cos 2 ⁡ ( π 2 z ) + 3 z + 1 2 sin 2 ⁡ ( π 2 z ) + 1 π ( 1 2 − cos ⁡ ( π z ) ) sin ⁡ ( π z ) + h ( z ) sin 2 ⁡ ( π z ) {\displaystyle...

Z-1 was a Japanese idol quartet signed under Toshiba EMI from 1999 to 2002. The name Z-1 signifies the last (Z) super stars of the 20th century and the...

Z (i.e. between negative infinity and Z). This table gives a probability that a statistic is greater than Z. f ( z ) = 1 − Φ ( z ) {\displaystyle f(z)=1-\Phi...

z: ∫ arcsin ⁡ ( z ) d z = z arcsin ⁡ ( z ) + 1 − z 2 + C ∫ arccos ⁡ ( z ) d z = z arccos ⁡ ( z ) − 1 − z 2 + C ∫ arctan ⁡ ( z ) d z = z arctan ⁡ ( z )...

the function Ψ ( z ) = cos ⁡ 2 π ( z 2 − z − 1 / 16 ) cos ⁡ 2 π z {\displaystyle \Psi (z)={\frac {\cos 2\pi (z^{2}-z-1/16)}{\cos 2\pi z}}} and its derivatives...

ψ ( z ) = d d z ln ⁡ Γ ( z ) = Γ ′ ( z ) Γ ( z ) . {\displaystyle \psi (z)={\frac {\mathrm {d} }{\mathrm {d} z}}\ln \Gamma (z)={\frac {\Gamma '(z)}{\Gamma...

Z n ) ( ℜ ( z 1 ) , ℑ ( z 1 ) , … , ℜ ( z n ) , ℑ ( z n ) ) = P ⁡ ( ℜ ( Z 1 ) ≤ ℜ ( z 1 ) , ℑ ( Z 1 ) ≤ ℑ ( z 1 ) , … , ℜ ( Z n ) ≤ ℜ ( z n ) , ℑ ( Z...

Z1, Z-1, or Z.1 may refer to: Z.1 or the Flow of Funds, a U.S. government fiscal report Z.1, an anti-tank barrier known as Admiralty scaffolding Z-1 (band)...

quickly: e z = 1 + 2 z 2 − z + z 2 6 + z 2 10 + z 2 14 + ⋱ {\displaystyle e^{z}=1+{\cfrac {2z}{2-z+{\cfrac {z^{2}}{6+{\cfrac {z^{2}}{10+{\cfrac {z^{2}}{14+\ddots...

defined as the (m + 1)th derivative of the logarithm of the gamma function: ψ ( m ) ( z ) := d m d z m ψ ( z ) = d m + 1 d z m + 1 ln ⁡ Γ ( z ) . {\displaystyle...

point z 0 {\displaystyle z_{0}} if the limit lim z → z 0 f ( z ) − f ( z 0 ) z − z 0 {\displaystyle \lim _{z\to z_{0}}{f(z)-f(z_{0}) \over z-z_{0}}} exists...

1 ( 1 , 1 ; 2 ; − z ) = ln ⁡ ( 1 + z ) z 2 F 1 ( a , b ; b ; z ) = ( 1 − z ) − a ( b  arbitrary ) 2 F 1 ( 1 2 , 1 2 ; 3 2 ; z 2 ) = arcsin ⁡ ( z ) z 2...

function B ( z 1 , z 2 ) = ∫ 0 1 t z 1 − 1 ( 1 − t ) z 2 − 1 d t = Γ ( z 1 ) Γ ( z 2 ) Γ ( z 1 + z 2 ) {\displaystyle \mathrm {\mathrm {B} } (z_{1},z_{2})=\int...

_{0}(z)={z \over 1-z}} Li − 1 ⁡ ( z ) = z ( 1 − z ) 2 {\displaystyle \operatorname {Li} _{-1}(z)={z \over (1-z)^{2}}} Li − 2 ⁡ ( z ) = z ( 1 + z ) ( 1 − z...

±1, ±2, ... ( 1 z d d z ) m ( z n + 1 f n ( z ) ) = z n − m + 1 f n − m ( z ) , ( 1 z d d z ) m ( z − n f n ( z ) ) = ( − 1 ) m z − n − m f n + m ( z )...

The atomic number or nuclear charge number (symbol Z) of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei composed of...

z ) = 2 z V ( z ) + z 2 U ( z ) + 1 V ( z ) = z U ( z ) + z 2 V ( z ) = z 1 − z 2 U ( z ) , {\displaystyle {\begin{aligned}U(z)&=2zV(z)+z^{2}U(z)+1...

Shawn Corey Carter (born December 4, 1969), known professionally as Jay-Z, is an American rapper and entrepreneur. Born and raised in New York City, he...

1 ) E ( X 2 ) = e μ 1 + σ 1 2 2 e μ 2 + σ 2 2 2 ) : e ( ( μ ^ 1 − μ ^ 2 + 1 2 S 1 2 − 1 2 S 2 2 ) ± z 1 − α 2 S 1 2 n 1 + S 2 2 n 2 + S 1 4 2 ( n 1 −...

1 3 [ Q x x − Q y y − Q z z Q y x + Q x y Q z x + Q x z Q z y − Q y z Q y x + Q x y Q y y − Q x x − Q z z Q z y + Q y z Q x z − Q z x Q z x + Q x z Q...

X_{k}=\sum _{n=0}^{N-1}x(n)z_{k}^{-n}} z k = A ⋅ W − k , k = 0 , 1 , … , M − 1 {\displaystyle z_{k}=A\cdot W^{-k},k=0,1,\dots ,M-1} where A is the complex...

= | z 0 | 2 + | z 1 | 2 + | z 2 | 2 + | z 3 | 2 ± ( | z 0 | 2 + | z 1 | 2 + | z 2 | 2 + | z 3 | 2 ) 2 − | z 0 2 − z 1 2 − z 2 2 − z 3 2 | 2 = | z 0 |...