Show that the following pairs of functions are orthogonal on [−1, 1]:(a) Any even function geven (x) = geven(-x) with any odd function hodd(x) = −hodd(-x).(b)P₂ and P4 (the second and fourth Legendre polynomials).

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Any even function geven(x) = geven (-x) with any odd function hodd(x) = −hodd(- P2 and P4 (the second and fourth Legendre polynomials).