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Display information for equation id:math.2653.16 on revision:2653

* Page found: Klein Gordon und Relativität (eq math.2653.16)

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TeX (original user input): 

\begin{align}

& {{\partial }_{x}}={{\partial }_{x}}\left( {{x}'} \right){{\partial }_{{{x}'}}}+{{\partial }_{x}}\left( {{t}'} \right){{\partial }_{{{t}'}}}=\gamma \,{{\partial }_{{{x}'}}}-\frac{\gamma \beta }{c}{{\partial }_{{{t}'}}} \\

& \partial _{x}^{2}={{\partial }_{x}}{{\partial }_{x}}=\left\{ \gamma \,{{\partial }_{{{x}'}}}-\frac{\gamma \beta }{c}{{\partial }_{{{t}'}}} \right\}\left\{ \gamma \,{{\partial }_{{{x}'}}}-\frac{\gamma \beta }{c}{{\partial }_{{{t}'}}} \right\} \\

& \partial _{t}^{2}\,\text{analog} \\

\end{align}

TeX (checked): 

{\begin{aligned}&{{\partial }_{x}}={{\partial }_{x}}\left({{x}'}\right){{\partial }_{{x}'}}+{{\partial }_{x}}\left({{t}'}\right){{\partial }_{{t}'}}=\gamma \,{{\partial }_{{x}'}}-{\frac {\gamma \beta }{c}}{{\partial }_{{t}'}}\\&\partial _{x}^{2}={{\partial }_{x}}{{\partial }_{x}}=\left\{\gamma \,{{\partial }_{{x}'}}-{\frac {\gamma \beta }{c}}{{\partial }_{{t}'}}\right\}\left\{\gamma \,{{\partial }_{{x}'}}-{\frac {\gamma \beta }{c}}{{\partial }_{{t}'}}\right\}\\&\partial _{t}^{2}\,{\text{analog}}\\\end{aligned}}

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MathML (36.649 KB / 3.79 KB) :

∂ x = ∂ x ⁡ ( x ′ ) ⁢ ∂ x ′ + ∂ x ⁡ ( t ′ ) ⁢ ∂ t ′ = γ ⁢ ∂ x ′ - γ ⁢ β c ⁢ ∂ t ′ ∂ x 2 = ∂ x ⁡ ∂ x = { γ ⁢ ∂ x ′ - γ ⁢ β c ⁢ ∂ t ′ } ⁢ { γ ⁢ ∂ x ′ - γ ⁢ β c ⁢ ∂ t ′ } ∂ t 2 ⁡ analog absent subscript 𝑥 subscript 𝑥 superscript 𝑥 ′ subscript superscript 𝑥 ′ subscript 𝑥 superscript 𝑡 ′ subscript superscript 𝑡 ′ 𝛾 subscript superscript 𝑥 ′ 𝛾 𝛽 𝑐 subscript superscript 𝑡 ′ absent superscript subscript 𝑥 2 subscript 𝑥 subscript 𝑥 𝛾 subscript superscript 𝑥 ′ 𝛾 𝛽 𝑐 subscript superscript 𝑡 ′ 𝛾 subscript superscript 𝑥 ′ 𝛾 𝛽 𝑐 subscript superscript 𝑡 ′ absent superscript subscript 𝑡 2 analog {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle{{\partial}_{x}}% ={{\partial}_{x}}\left({{x}^{\prime}}\right){{\partial}_{{{x}^{\prime}}}}+{{% \partial}_{x}}\left({{t}^{\prime}}\right){{\partial}_{{{t}^{\prime}}}}=\gamma% \,{{\partial}_{{{x}^{\prime}}}}-\frac{\gamma\beta}{c}{{\partial}_{{{t}^{\prime% }}}}\\ \par&\displaystyle\partial_{x}^{2}={{\partial}_{x}}{{\partial}_{x}}=\left\{% \gamma\,{{\partial}_{{{x}^{\prime}}}}-\frac{\gamma\beta}{c}{{\partial}_{{{t}^{% \prime}}}}\right\}\left\{\gamma\,{{\partial}_{{{x}^{\prime}}}}-\frac{\gamma% \beta}{c}{{\partial}_{{{t}^{\prime}}}}\right\}\\ \par&\displaystyle\partial_{t}^{2}\,\text{analog}\\ \par\end{aligned}}}

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MathML (4.194 KB / 489 B) :

∂x=∂x(x′′)∂x′′+∂x(t′′)∂t′′=γ∂x′′−γβc∂t′′∂x2=∂x∂x={γ∂x′′−γβc∂t′′}{γ∂x′′−γβc∂t′′}∂t2analog

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