The function defined by T(m, n, r) congruent r^(2n - m + 1) e^(-r^2) (Γ(1/2 m + 1/2))/(n!) _1 F_1(1/2(m + 1);n + 1;r^2) (Heatley 1943, p. 509), where _1 F_1(a;b;z) is a confluent hypergeometric function of the first kind and Γ(z) is the gamma function. Heatley originally defined the function in terms of the integral T(m, n, p, a) = integral_0^∞ t^(-n) e^(-p^2 t^2) I_n(2a t) d t, where I_n(x) is a modified Bessel function of the first kind, which is similar to an integral of Watson, with Watson's J_ν(a t) changed to I_n(2a t) and a few other minor changes of variables.
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