Toronto function

In mathematics, the Toronto function is a modification of the confluent hypergeometric function defined by A. H. Heatley as^[1][2]

${\displaystyle T(m,n,r)=r^{2n-m+1}{e}^{-r^2}\frac{\mathrm{\Gamma }(\frac{1}{2}m+\frac{1}{2})}{\mathrm{\Gamma }(n+1)}{}_1{F}_1(\frac{1}{2}m+\frac{1}{2};n+1;r^2),}$

where ${\displaystyle \mathrm{\Gamma }}$ is the gamma function and ${}_1{F}_1$ is a confluent hypergeometric function of the first kind.

The Toronto function has appeared in a study on the theory of turbulence.^[3]

• Weisstein, Eric W.. "Toronto function". https://mathworld.wolfram.com/TorontoFunction.html. 

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