Z 2N series information

The Z 2N (French: Automotrice Z à 2 niveaux, English: two-level Z series) is a family of double-deck electric multiple unit trainsets that are operated...

produced as part of the Z 2N series of trainsets, which were continuously improved over several generations. The introduction of the Z 20900 allowed for the...

in length and nearly identical to those used on the earlier Z 2N series trainsets (Z 5600/Z 8800) and the VB2N. After 1991, the consortium started delivering...

continuously improved over several generations. The Z 2N series was also the basis of the later MI 2N family of double-deck, dual power trainsets. After...

distances. The Z 23500 serie is the first generation of TER 2N séries followed in 2004 by the Z 24500/ Z 26500 series also called TER 2N NG. Following...

_{k=1}^{n}k^{2}z^{k}=z{\frac {1+z-(n+1)^{2}z^{n}+(2n^{2}+2n-1)z^{n+1}-n^{2}z^{n+2}}{(1-z)^{3}}}} ∑ k = 1 n k m z k = ( z d d z ) m 1 − z n + 1 1 − z {\displaystyle...

The SNCF Class Z 22500, also known as the MI 2N "Eole" or MI 2N (French: Matériel d'Interconnexion à 2 Niveaux, Est Ouest Liaison Express, English: two-level...

}{\frac {[(2n)!]^{2}}{16^{n}(n!)^{4}}}x^{2n}\\{\frac {2}{\pi }}E(x)&=\sum _{n=0}^{\infty }{\frac {[(2n)!]^{2}}{(1-2n)16^{n}(n!)^{4}}}x^{2n}\end{aligned}}}...

opportunity, with the Z 20500s, to travel to the Transilien Paris Saint-Lazare network. Finally, due to the renovation of the VB 2N trainsets since 2003...

stock: 2N (French: 2 Niveaux, English: two-level). Bombardier brands this equipment as the OMNEO and SNCF classes it as Z 55500, Z 56300, Z 56500, Z 56600...

{d} z^{m+1}}}\ln \Gamma (z).} Thus ψ ( 0 ) ( z ) = ψ ( z ) = Γ ′ ( z ) Γ ( z ) {\displaystyle \psi ^{(0)}(z)=\psi (z)={\frac {\Gamma '(z)}{\Gamma (z)}}}...

{(-1)^{n}z^{2n+1}}{n!(2n+1)}}\\[6pt]&={\frac {2}{\sqrt {\pi }}}\left(z-{\frac {z^{3}}{3}}+{\frac {z^{5}}{10}}-{\frac {z^{7}}{42}}+{\frac {z^{9}}{216}}-\cdots...

) n ( q z ) n {\displaystyle \displaystyle {}_{r+1}V_{r}(a_{1};a_{6},a_{7},...a_{r+1};q,p;z)=\sum _{n=0}^{\infty }{\frac {\theta (a_{1}q^{2n};p)}{\theta...

{(-1)^{n}x^{2n+1}}{(2n+1)!}}=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots ,} valid for all real x. These power series are also examples...

π z ) . {\displaystyle f(z)=\sum _{n=0}^{\infty }\left[A_{n}(1-z)f^{(2n)}(0)+A_{n}(z)f^{(2n)}(1)\right]+\sum _{k=1}^{N}C_{k}\sin(k\pi z).} Here An(z) is...

mathematics, the Laurent series of a complex function f ( z ) {\displaystyle f(z)} is a representation of that function as a power series which includes terms...

{1}{2N}},{\frac {3}{2N}},\cdots ,{\frac {N-4}{2N}},{\frac {N-2}{2N}},{\frac {N+2}{2N}},{\frac {N+4}{2N}},\cdots ,{\frac {2N-3}{2N}},{\frac {2N-1}{2N}};\\[8pt]{\frac...

&a_{n-1}\\a_{1}&a_{2}&&&\vdots \\a_{2}&&&&a_{2n-4}\\\vdots &&&a_{2n-4}&a_{2n-3}\\a_{n-1}&\ldots &a_{2n-4}&a_{2n-3}&a_{2n-2}\end{bmatrix}}.} In terms of the components...

{(-1)^{n}}{(2n+1)!}}x^{2n+1},\\\cos x&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n)!}}x^{2n}.\end{aligned}}} Using the multiplication formula for power series at...

are also known as TER 2N NG from their use on regional TER services, bi-level design (2N), and, by replacing the SNCF Class Z 23500, status as a "new...

{1}{\prod _{n>0}(1-q^{n})}}\sum _{n\in \mathbf {Z} }{\frac {(-1)^{n}(1+q^{n})q^{n(3n+1)/2}}{1+q^{2n}}}} (sequence A053250 in the OEIS). ψ ( q ) = ∑ n...

computing (z-m)/v1/2, yields: z − artanh ⁡ ( ρ ) − ρ 2 N 1 N + 6 − ρ 2 2 N 2 {\displaystyle {\frac {z-\operatorname {artanh} (\rho )-{\frac {\rho }{2N}}}{\sqrt...

{z^{3}}{3}}+{\frac {z^{5}}{5}}-{\frac {z^{7}}{7}}+\cdots =\sum _{n=0}^{\infty }{\frac {(-1)^{n}z^{2n+1}}{2n+1}}\,;\qquad |z|\leq 1\qquad z\neq i,-i} Series for the...

0+\zeta (2n+1)-\zeta (2n+1)=0} . The same trick can be used to establish the sum of the Eisenstein series: π cot ⁡ ( π z ) = lim N → ∞ ∑ n = − N N ( z − n...

_{n=0}^{\infty }{\frac {U_{2n+1}}{(2n+1)!}}x^{2n+1}\\[8mu]&{}=\sum _{n=1}^{\infty }{\frac {(-1)^{n-1}2^{2n}\left(2^{2n}-1\right)B_{2n}}{(2n)!}}x^{2n-1}\\[5mu]&{}=x+{\frac...