oronto Function
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
10-6-2019
1755
oronto Function
The function defined by
 |
(1)
|
(Heatley 1943; Abramowitz and Stegun 1972, p. 509), where 
is a confluent hypergeometric function of the first kind and 
is the gamma function.
Heatley originally defined the function in terms of the integral
 |
(2)
|
where 
is a modified Bessel function of the first kind, which is similar to an integral of Watson (1966, p. 394), with Watson's 
changed to 
and a few other minor changes of variables. In terms of this function,
 |
(3)
|
(Heatley 1943). Heatley (1943) also gives a number of recurrences and other identities satisfied by 
.
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 509, 1972.
Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 1. New York: Krieger, p. 268, 1981.
Heatley, A. H. "A Short Table of the Toronto Function." Trans. Roy. Soc. Canada 37, 13-29, 1943.
Slater, L. J. Confluent Hypergeometric Functions. Cambridge, England: Cambridge University Press, p. 99, 1960.
Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.
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