where E[n,z] = [[integral].sup.[infinity].sub.1] [t.sup.-n] [e.sup.-zt] is '
exponential integral function'.
Salem, "A q-analogue of the
exponential integral," Afrika Matematika, vol.
However, the incomplete gamma function is a more complete way to calculate the temperature integral than the
exponential integral because [p.sub.m](x) = [LAMBDA](-(m + 1),x) yielded consistent results (low errors) for any m, integer or non-integer in the interval 1 [less than or equal to] x [less than or equal to] 100 tested in the supplementary material.
Among the topics are complete elliptic integrals, the Riemann zeta function, some automatic proofs, the error function, hyper-geometric functions, Bessel-K functions, polylogarithm functions, evaluation by series, the
exponential integral, confluent hyper-geometric and Whittaker functions, and the evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets.
where [[bar.[gamma]].sub.bm] = [P.sub.b]/[[sigma].sup.2.sub.m] and [E.sub.1] (x) = [[integral].sup.[infinity].sub.x]([e.sup.-t]/t)dt is the
exponential integral function.
A.1 Mathematical tools:
Exponential integral, sine integral and cosine integral
For indefinite integrals, an extended version of the Risch code is used whenever both the integrand and integral can be expressed in terms of elementary functions,
exponential integral functions, polylogarithms and other related functions.
and ExpIntegral E[n, z] gives the
exponential integral function [E.sub.n] (z), which is defined by
Exponential Integral, Logarithmic Integral, Sine and Cosine Integrals
In Section 2, we provide an explicit expression of the moment generating function in terms of the
exponential integral function.
We define, for x > 0, the function F(x) = x[e.sup.x][E.sub.1](x), where [E.sub.1] (x) denotes the
exponential integral ([1], (5.1.1)).
Uniform convergence and computation of the generalized
exponential integrals. J.
