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^{2 n - m + 1} e^{- r^{2}} \frac{Γ (\frac{1}{2} m + \frac{1}{2})}{Γ (n + 1)}_{1} F_{1} (\frac{1}{2} m + \frac{1}{2}; n + 1; r^{2}),

where $Γ$ 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.

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