Toronto function explained

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

T(m,n,r) = r ^{2n-m+1} e ^{- r ^{2}} (\Gamma( (1 { 2)/())/(m + (1 { 2 })}{\Gamma(n +1 )}{})/(_{1F})) ^{1 ({ style (1{2}}m+{ style (1{2}};n+1;r)/(^{2).}))/()}

Later, Heatley (1964) recomputed to 12 decimals the table of the M(R)-function, and gave some corrections of the original tables. The table was also extended from x = 4 to x = 16 (Heatley, 1965). An example of the Toronto function has appeared in a study on the theory of turbulence (Heatley, 1965).

References

• • Heatley, A. H. (1964), "A short table of the Toronto function", Mathematics of Computation, 18, No.88: 361
• Heatley, A. H. (1965), "An extension of the table of the Toronto function", Mathematics of Computation, 19, No.89: 118-123
• Weisstein, E. W., "Toronto Function", From Math World - A Wolfram Web Resource