mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, 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 ...

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