Toronto function

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

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

where $\mathrm{\Gamma }$ 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.

References

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

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

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

External links

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