Toronto function

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title: "Toronto function" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["special-hypergeometric-functions"] topic_path: "general/special-hypergeometric-functions" source: "https://en.wikipedia.org/wiki/Toronto_function" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

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}\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). :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

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