The Calculus of Finite Differences |
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a₁ absolutely convergent arbitrary periodic B₁ B₂ Bernoulli's polynomials c₁ coefficients column consider constant continued fraction convergence abscissa corresponding denote derivate determine difference equation differential divided differences error Euler's example expression factorial series finite Gauss given half-plane Hence holomorphic indicial equation integral interpolation formula interval linear method multiplier Newton's series Nörlund notation numbers obtain operator P₁ partial fractions particular solution polynomial polynomial of degree positive integer principal solution Prove R₁ R₂ rational function reciprocal differences remainder term result series converges shew Stirling's formula summation suppose Thiele's Thiele's interpolation formula u₁ u₁(x u₂ unity Ux+1 v₂ values vanish variable w₁ whence write x₁ Xn+1 y₁ zero α₁