The Coefficients of Multivalent Close-to-Convex Functions

2t (n + p) !. . (1. 1) \ = D tí (p + t) \ (p -/) ! (» -P -l) ! (w2 -t2) Inequality (1. 1) reduces to the well-known Bieberbach conjecture when p -l. The conjecture was proven by Goodman and Robertson 3 for a function in S (p), in case all its coefficients are real and by Robertson 7, in case di = a2= • • ■ =ap₂ = 0, the remaining coefficients being complex. The author 5 proved (1. 1) for n = p + l for functions in 3C (p), no restrictions being made on the coefficients. In this paper, we will prove (1. 1) for functions of the class X, (p) for the case <ïi = a2= • • ■ =aj, ₂ = 0, the remaining coefficients being complex. The case p -2 of our proof gives (1. 1) for the entire class 3C (2). Inequality (1. 1) is known to be true for the class 3C (1) ó.