The incomplete beta function
Victor H. Moll · 2014
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].