Toronto function

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.

References

• Heatley, A. H. (1943). "A short table of the Toronto function". Transactions of the Royal Society of Canada. 37: 13–29. MR 0010055.

• Heatley, A. H. (1964). "Table errata 361: "A short table of the Toronto function"". Mathematics of Computation. 18 (88): 687–688. JSTOR 2002973.

• Heatley, A. H. (1965). "An extension of the table of the Toronto function". Mathematics of Computation. 19 (89): 118–123. JSTOR 2004105.

External links

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