mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, the Toronto function ''T''(''m'',''n'',''r'') is a modification of the

confluent hypergeometric function In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular s ...

defined by , Weisstein, as :

T(m,n,r)=r^e^\frac_1F_1(m+;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

*{{Citation , last1=Heatley , first1=A. H. , title=A short table of the Toronto function , mr=0010055 , year=1943 , journal=Trans. Roy. Soc. Canada Sect. III. , volume=37 , pages=13–29 *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 Special hypergeometric functions