## A generalization of completely convex functions |

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_ _ I I _ _I _ 0 _ _ 4 _ _ I _ _ I I _ _ I I I I _ l _ _ Lemma _ O.A _ Prepared _ Proof __ _I _ a+3b agency and/or monitoring and/or monitoring agency attains its maximum Boas and Polya Completely Convex Functions constant defined dx dy entire function exponential type extend Widder's theorem f f(x fKfJ°(ar function f(x function of exponential gg f(x H I _ Hence I I I _ _ I4 _ IA x IA intermediate derivatives interval a,b Jo(ar Lemma 2 applies Let xo maximum of f(2)(x means of Lemma Originating agency and/or PENNSYLVANIA STATE UNIVERSITY possesses derivatives q _ _ result follows satisfies condition Taylor expansion Unclassified unit circle variable Widder wx dx