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Toronto function

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Source updated September 11, 2026

In mathematics, the Toronto function is a modification of the confluent hypergeometric function defined by A. H. Heatley as

$T(m,n,r)=r^{2n-m+1}e^{-r^{2}}{\frac {\Gamma {\big (}{\frac {1}{2}}m+{\frac {1}{2}}{\big )}}{\Gamma (n+1)}}{}_{1}F_{1}{\big (}{\textstyle {\frac {1}{2}}}m+{\textstyle {\frac {1}{2}}};n+1;r^{2}{\big )},$

where $\Gamma$ 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.

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