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lambdak

Evaluate lambda function for Affine Wigner distribution.

Calling Sequence

Y = lambdak(U,K)

Parameters

U :

real vector

K :

real scalar

Y :

value of LAMBDAD at point(s) U

Description

lambdak evaluates the parametrization lambda function involved in the affine smoothed pseudo Bertrand distribution. lambdak(U,0) = -U/(exp(-U)-1) for K = 0 lambdak(U,1) = exp(1+U exp(-U)/(exp(-U)-1)) for K = 1 lambdak(U,K) = (K (exp(-U)-1)/(exp(-KU)-1))^(1/(K-1)) otherwise

Examples

u=linspace(0.001,5,100)';
clf;plot(u,[lambdak(u,0),lambdak(u,1),lambdak(u,2)])
legend("k="+["0","1","2"]);

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