It is known that some special functions can be represented as corresponding Laplace transforms, for example, Binet formula for gamma function:lnΓ(z)−(z−12)lnz+z−12ln(2π)=∫0∞(1et−1−1t+12
For 伪 = 1, the Erlang functions are particular cases of the lower/upper incomplete gamma functions 螕(a, x), corresponding to integer values a = n of the parameter. Note that the lower one equals also a鈭 1xae鈭抶F1,1(1, 1 + a; x) where F1,1(1, 1 + a; x) is the ...
In the case when ζ = zw¯ belongs to the sector | arg(ζ − 1)| < 3π 4 , the result can alternatively be deduced by writing the kernel as a product involving an incomplete gamma-function and appealing to an asymptotic result due to Tricomi [75]. Our present approach (found ...
Qi, F.: Monotonicity results and inequalities for the gamma and incomplete gamma functions. Math. Inequal. Appl. 5(1), 61–67 (2002) MathSciNet MATH Google Scholar Qi, F., Cui, L.H., Xu, S.L.: Some inequalities constructed by Tchebysheff’s integral inequality. Math. Inequal. ...
It is possible that reward information is not ubiquitously distributed when these task requirements are not in place, since outcomes resulting from nonchoice events may not be deemed as important as those that do (Tricomi et al., 2004, O'Doherty et al., 2004). This needs to be tested in...
In the framework of the theory of linear viscoelasticity, we derive an analytical expression of the relaxation modulus in the Andrade model Gαt for the case of rational parameter α=m/n∈(0,1) in terms of Mittag–Leffler functions from its Laplace trans
Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F.G. Higher Transcendental Functions; Vol. I. Based on notes left by Harry Bateman. With a preface by Mina Rees. With a foreword by E. C. Watson. Reprint of the 1953 original; Robert E. Krieger Publishing Co., Inc.: ...