Toronto function

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In mathematics, the Toronto function T(m,n,r) is a modification of the confluent hypergeometric function defined by Heatley (1943) as

T(m,n,r)=r^{2n-m+1}e^{-r^2}\frac{\Gamma(\frac 1{2}m+\frac 1{2})}{\Gamma(n+1)}{}_1F_1({\textstyle\frac 1{2}}m+{\textstyle\frac 1{2}};n+1;r^2).


  • Heatley, A. H. (1943), "A short table of the Toronto function", Trans. Roy. Soc. Canada Sect. III. 37: 13–29, MR 0010055