Toronto function

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

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

where ${\displaystyle \Gamma }$ is the gamma function and ${\displaystyle _{1}F_{1}}$ is a confluent hypergeometric function of the first kind.

The Toronto function has appeared in a study on the theory of turbulence.

References

External links

• Weisstein, Eric W. "Toronto function". MathWorld.

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