CÁLCULO FINITO: DEMONSTRAÇÕES E APLICAÇÕES - (:unkn) unknown (UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2014)
In this work some topics of the Discrete or Finite Calculus are developed. In particular, we study difference operators, factorial powers, Stirling numbers of the first and second type, the Newton’s formula of differences, the fundamental theorem of the Finite Calculus, the summation process, and the Bernoulli numbers and Bernoulli polynomials. Then we show the effectiveness of the theory for the calculation of closed formulas for the value of many finite sums. We also study the classical problem of obtaining the polynomials which express the value of the sums of powers of natural numbers.
Keywords: cálculo finito ou discreto; números de Stirling; somação; números de Bernoulli; polinômios de Bernoulli; finite or discrete calculus; Stirling numbers; summation; Bernoulli Numbers; Bernoulli polynomials; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA