of 10 auestions left this cycle. Yk+1 - Yk = E amk", (2.60) m=0 where the am are given constants, can have its solution expressed in terms of Bernoulli polynomials. Note that the Bernoulli polynomials...

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Extracted text: of 10 auestions left this cycle. Yk+1 - Yk = E amk", (2.60) m=0 where the am are given constants, can have its solution expressed in terms of Bernoulli polynomials. Note that the Bernoulli polynomials are expressed as functions of k with B (k) being of degree n. It is also possible to express k" as a sum of Bernoulli polynomials. Using the results given above we obtain k = B1(k) + /½, k2 = B2(k) + B1(k) + /3, k3 = B3(k) + 3/½B2(k) + B1(k) + ½, k4 = B4(k) + 2B3(k) + 2B2(k) + B1(k) + 19/30, etc. It can be shown that k" has the following expansion: 1 n+1 i B:(k). (2.61) n+1 i=0