k = B(k) + 1/2, k2 = B2(k) + B1(k)+ /3, k3 = B3(k) + /2B2(k) + B1(k) + ½, k = B4(k) + 2B3(k) +2B2(k) + B1(k) + 19/30, %3D etc. It can be shown that k" has the following expansion: B:(k). (2.61) n+12 i=0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
Transcribed Image 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
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