Geodesic
ON BRANNAN'S COEFFICIENT CONJECTURE AND APPLICATIONS
Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 45-52

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D. Brannan's conjecture says that for 0 <α,β≤1, |x|=1, and n∈N one has |A2n−1(α,β,x)|≤|A2n−1(α,β,1)|, whereWe prove this for the case α=β, and also prove a differentiated version of the Brannan conjecture. This has applications to estimates for Gegenbauer polynomials and also to coefficient estimates for univalent functions in the unit disk that are ‘starlike with respect to a boundary point’. The latter application has previously been conjectured by H. Silverman and E. Silvia. The proofs make use of various properties of the Gauss hypergeometric function.
DOI : 10.1017/S0017089507003400
Mots-clés : Primary 30C50, Secondary 33C05, 33C45 
RUSCHEWEYH, STEPHAN; SALINAS, LUIS. ON BRANNAN'S COEFFICIENT CONJECTURE AND APPLICATIONS. Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 45-52. doi: 10.1017/S0017089507003400
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