ABSTRACT
Γ′(x) Γ(x)
, (11.1.2)
and define β(x) by the identity
β(x) = 1
( ψ ( x+1 2
)− ψ (x2 )) . (11.1.3) This definition appears as 8.370 and (11.1.1) appears as 3.222.1. Here
Γ(x) =
tx−1e−t dt (11.1.4)
is the classical gamma function. Naturally, both starting points for β are equivalent, and Corollary 11.2.1 proves (11.1.3). The value
γ ′
In this chapter we will prove elementary properties of this function and use them to evaluate some definite integrals in [40].
