Β(1 – X) = (-1)*B(X) B(X + 1) - B,(X) = kX*-1 Σ B (x + + (x + ²) = q²¹* B₂ (qX). 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Proposition 7.1. Let B(X) be Bernoulli polynomial defined above and q be any positive
integer. We have following identities
B. (1X) = (-1)k Bk. (X)
Bk (X+1) - Bk (X) = kXk-¹
Σ Be (x + ²) = q + Ba(qX).
0<a<q
From equation 2 we conclude that B₁(1) = B₁(0) for n > 2.
Transcribed Image Text:Proposition 7.1. Let B(X) be Bernoulli polynomial defined above and q be any positive integer. We have following identities B. (1X) = (-1)k Bk. (X) Bk (X+1) - Bk (X) = kXk-¹ Σ Be (x + ²) = q + Ba(qX). 0<a<q From equation 2 we conclude that B₁(1) = B₁(0) for n > 2.
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