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I am puzzled how the linear interpolation functions (see attached) were determined based on the following equation below

##\displaystyle \psi_i=\frac{(\xi-\xi_1)(\xi-\xi_2)....(\xi-\xi_{i-1})(\xi-\xi_{i+1})...(\xi-\xi_n)}{(\xi_i-\xi_1)(\xi_i-\xi_2)...(\xi_i-\xi_{i-1})(\xi_i-\xi_{i+1})...(\xi_i-\xi_n)}##

What do the dots represent above?

and

[itex]\psi_i(\xi_j)= 1[/itex] if ##i=j## and ##0## if ##i\ne j##

For example how is ##\psi_1(\xi)## determined?

thanks

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# Derivation of Lagrange Family of Interpolation functions

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