...} { a } \frac { z - a } { 1 - \overline { a } z } , \quad | a | < 1, \end{equation*}
...1 - \overline { a } z } , \quad \sum ( 1 - | a _ { j } | ) < \infty . \end{equation*}
3 KB (432 words) - 20:48, 22 January 2024
...^ { k } } { ( 2 k + 1 ) ^ { 2 } } \approx0.915965594177219015 \ldots. \end{equation}
...Gamma ( z ) \} = \frac { \Gamma ^ { \prime } ( z ) } { \Gamma ( z ) } \end{equation}
4 KB (577 words) - 14:03, 11 November 2023
$#C+1 = 29 : ~/encyclopedia/old_files/data/H110/H.1100380 Hutchinson equation
...males is taken as the unit of time. This equation is called the Hutchinson equation. For $ \lambda < {\pi / 2 } $,
4 KB (552 words) - 22:11, 5 June 2020
is the equation of $ \gamma $,
then the equation of its evolute has the form
3 KB (450 words) - 19:38, 5 June 2020
..._ { \zeta \in T } \sqrt { \operatorname { area } ( K _ { \zeta } ) }. \end{equation*}
5 KB (668 words) - 17:47, 1 July 2020
...8 : ~/encyclopedia/old_files/data/N067/N.0607040 Non\AAhFredholm integral equation
...lse. Sometimes such an integral equation is said to be a singular integral equation.
3 KB (465 words) - 15:24, 28 February 2022
Usually, the matrix equation
\begin{equation} \tag{a1} A ^ { * } X + X A + C = 0, \end{equation}
5 KB (876 words) - 16:52, 1 July 2020
...{ i \theta }) \overline { g ( e ^ { i \theta } ) } d \mu ( \theta ), \end{equation*}
...= z \Phi _ { n } ( z ) + \rho _ { n + 1 } \Phi _ { n } ^ { * } ( z ), \end{equation*}
7 KB (1,105 words) - 10:02, 11 November 2023
...f. also [[Differential equation, partial, of the second order|Differential equation, partial, of the second order]]). Boundary conditions of the form
810 bytes (116 words) - 14:55, 16 October 2014
\begin{equation} \tag{a1} S _ { 0 } = 0, \end{equation}
...f } S _ { k } \leq t < S _ { k + 1 } \;\text { for } k = 0,1, \dots , \end{equation*}
10 KB (1,526 words) - 19:03, 23 January 2024
$#C+1 = 34 : ~/encyclopedia/old_files/data/U095/U.0905870 Urysohn equation
A non-linear integral equation of the form
3 KB (455 words) - 08:27, 6 June 2020
...n*} X ^ { \prime \prime } ( t ) + \mathcal{R} ( t ) \circ X ( t ) = 0 \end{equation*}
\begin{equation*} X ( s ) = 0 , X ^ { \prime } ( s ) = I. \end{equation*}
2 KB (315 words) - 16:46, 1 July 2020
A second-order ordinary linear differential equation:
...rgeometric equation]]. The substitution $y=u\exp(-x^2/4)$ converts Weber's equation into
2 KB (288 words) - 20:16, 28 January 2020
...}R(X,Y)=-R(Y,X),\\g(R(X,Y)Z,W)=g(R(Z,W)X,Y),R(X,Y)Z+R(Y,Z)X+R(Z,X)Y=0,\end{equation}
\begin{equation}J(\pi)=J(X_1)+...+J(X_r).\end{equation}
5 KB (875 words) - 18:06, 5 February 2021
...f. also [[Differential equation, partial, of the second order|Differential equation, partial, of the second order]]). Boundary conditions of the type
885 bytes (129 words) - 07:13, 23 August 2014
is locally defined by an equation $ F( x, y, z) = \textrm{ const } $,
satisfies the partial differential equation
2 KB (385 words) - 08:28, 6 June 2020
The Kufarev differential equation
...{ \partial f ( z , t ) } { \partial t } = - f ( z , t ) p ( f , t ), \end{equation}
11 KB (1,584 words) - 18:54, 24 January 2024
See also [[Volterra equation|Volterra equation]].
520 bytes (95 words) - 19:03, 27 April 2014
...ication is defined by the associativity and distributivity laws and by the equation $ ax = xa ^ {S} $
...carried out in the ordinary way while multiplication is determined by the equation $ ax = xa + a \prime $,
5 KB (880 words) - 19:00, 9 January 2024
An algebraic equation of degree three, ''i.e.'' an equation of the form
where $a\ne 0$. Replacing $x$ in this equation by the new unknown $y$
2 KB (312 words) - 19:38, 15 March 2023