TeXipedia

varSigma

Represents a capital sigma variant commonly used in mathematical notation to denote summations or specialized mathematical concepts.

Overview

Serves as an alternative form of the capital sigma symbol, offering a distinct visual appearance that helps differentiate between similar mathematical concepts.

  • Often employed in advanced mathematics to represent specialized operators or custom summations
  • Particularly useful when multiple sigma symbols appear in the same expression
  • Frequently seen in theoretical mathematics, statistics, and mathematical physics
  • Helps avoid ambiguity when regular Sigma is already used with another meaning in the same context

Examples

Sum of variances in statistical analysis.

Σi=1n(xi−μ)2=σ2n\varSigma_{i=1}^{n} (x_i - \mu)^2 = \sigma^2 n 
\varSigma_{i=1}^{n} (x_i - \mu)^2 = \sigma^2 n

Covariance matrix notation in multivariate statistics.

Σ=(σ12σ12σ21σ22)\varSigma = \begin{pmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{21} & \sigma_2^2 \end{pmatrix} 
\varSigma = \begin{pmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{21} & \sigma_2^2 \end{pmatrix}

Total system entropy in thermodynamics.

ΔStotal=ΣiΔSi\Delta S_{total} = \varSigma_i \Delta S_i 
\Delta S_{total} = \varSigma_i \Delta S_i