Some Expansions in Vector Space |
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Abel's theorem absolutely convergent analytic at T=0 analytic func analytic function b₁ B₂ complex number continuous functions COROLLARY defined definies an analytic Definition differential equation 6.3 EXPANSIONS B(T Fasc follows immediately Fréchet differential functions B(T Hence homogeneous polynomial hypothesis inequalities 6.1 Integrate 8.4 inverse given Journ least unity left hand inverse Lemma taking less than unity linear continuous operation linear vector space log D(T max|T(x modulus nò a,(T non-negative real numbers number system obtain PENNSYLVANIA STATE UNIVERSITY polynomial of degree postulates power series precisely the coefficient Proof properties proved elsewhere R. S. MARTIN radii of analyticity radii of convergence radius RECCURENT recurrence formulæ 3.1 recursion formula respectively right hand inverse rotation satisfies sequence of non-negative similar argument T+2U T₁ Taking norms tend to zero Theorem 3.I THEOREM 5.III theorem is proved tions transposed unique unit circle vector space V,(A