To solve the gamma function \Gamma(5/4), it is essential to understand that the gamma function generalizes the factorial and can be expressed through an integral representation. The discussion highlights the use of the integral \Gamma(x) = ∫(0,∞) t^(x-1)e^(-t) dt for x > 0, and how it can be simplified using the beta function. The relationship \beta(5/4, 3/2) = \Gamma(5/4)Γ(3/2)/Γ(4) is explored, but \Gamma(5/4) itself does not have a simple expression, as \Gamma(1/4) is known to be transcendental. Additionally, Euler's reflection formula is mentioned, which relates gamma functions at complementary arguments, providing insights into the nature of \Gamma(0) and its complexities. Understanding these relationships is crucial for evaluating gamma functions effectively.