Unrestricted.2016-11-142011-01-112016-11-142010-12http://hdl.handle.net/2346/ETD-TTU-2010-12-1150We discuss the Brannan Conjecture, which is an inequality on the coefficients of odd index of a certain power series, which depend on two other variables. The conjecture is introduced in the current format in 1972 and only verified for the odd indices 3,5 and 7. Here we employ a general squaring method and introduce some conjectures on the residue. By verifying our own conjectures using MATHEMATICA only for symbolic algebraic manupulations, we verify the Brannan Conjecture for all odd numbers upto 51. This maximal number is only limited by computational difficulties.application/pdfengBrannan conjectureCoefficientSquaringResidueMathematicaThesis