Alternative Equation Formats

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MathML

c m , n , N ( r ) = 2 ( N − n + 1 ) ( N − n ) ∑ s = n N ∑ t = s + 1 N ∏ j = 0 m − 1 I r ( z s − j , z t − j ) I r ( z s , z t ) = { 1 if  | z s − z t | < r 0 otherwise σ m , T 2 ( r ) = 4 ( k m + 2 ∑ j = 1 m − 1 k m − j c 2 j + ( m − 1 ) 2 c 2 m − m 2 k c 2 m − 2 ) c = c 1 , 1 , T ( r ) k = k T ( r ) = 6 T ( T − 1 ) ( T − 2 ) ∑ t = 1 T ∑ s = t + 1 T ∑ l = s + 1 T h r ( z t , z s , z l ) h r ( z t , z s , z l ) = 1 3 ( I r ( z t , z s ) I r ( z s , z l ) + I r ( z t , z l ) I r ( z l , z s ) + I r ( z s , z t ) I r ( z t , z l ) )

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Math as LaTeX Source

\begin{align*} c_{m,n,N}(r)& =\frac{2}{(N-n+1)(N-n)}\sum _{s=n}^{N}\sum _{t=s+1}^{N}\prod _{j=0}^{m-1}I_ r(z_{s-j},z_{t-j}) \\ I_ r(z_{s},z_{t})& =\left\{ \begin{array}{ l l } 1 & \text {if } |z_ s-z_ t|<r \\ 0 & \text {otherwise} \end{array} \right. \\ \sigma _{m,T}^{2}(r)& =4\left(k^ m+2\sum _{j=1}^{m-1}{k^{m-j}c^{2j}}+(m-1)^2c^{2m}-m^2kc^{2m-2}\right) \\ c& =c_{1,1,T}(r) \\ k& =k_ T(r)=\frac{6}{T(T-1)(T-2)}\sum _{t=1}^{T}\sum _{s=t+1}^{T}\sum _{l=s+1}^{T}{h_ r(z_ t,z_ s,z_ l)} \\ h_ r(z_ t,z_ s,z_ l)& =\frac{1}{3}\left(I_ r(z_ t,z_ s)I_ r(z_ s,z_ l)+I_ r(z_ t,z_ l)I_ r(z_ l,z_ s)+I_ r(z_ s,z_ t)I_ r(z_ t,z_ l)\right) \end{align*}
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