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Is the hypergeometric function $F(5/4,3/4; 2, z)$ bounded on $(0,1]$
Consider the classical hypergeometric function $F(5/4,3/4; 2, z)$ for $z\in (0,1]$. Is this bounded by some real number (independent of $z$)?
I'm aware of Euler's formula:
$$F(5/4,3/4; 2, z) = ...
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Bound for the Legendre function of the second kind of degree $1/2$
Let $Q_{1/2}(u)$ be the Legendre function of the second kind of degree $1/2$.
One can show that $Q_{1/2}(u) = O(u^{-3/2})$ as $u\to \infty$; see Equation 21 in Section 3.9.2 of Higher transcendental ...
