a) Now consider another function g(x) expanded in the above basis as (inluded in image).Prove that (in image)b) Now consider a non-orthonormal basis {Xn} for this space, such (included in image) Generalise the previous result to find an expression for (f|g) in terms of Snm. Confirm that if(included in image), then this result reduces to the above one. b) Now consider another function g(x) expanded in the above basis as g(x) = Σn dnon (T).Prove that (flg) = Σn endn.c) Now consider a non-orthonormal basis {x} for this space, such that (xmlXn) = Smn. Gen-eralise the previous result to find an expression for (flg) in terms of Snm. Confirm that ifSmn = 8mn, then this result reduces to the above one.

As per the question we are given a function g(x) expanded in the basis φn(x) and we have to prove…

a) Now consider another function g(x) expanded in the above basis as (inluded in image). Prove that (in image) b) Now consider a non-orthonormal basis {Xn} for this space, such (included in image) Generalise the previous result to find an expression for (f|g) in terms of Snm. Confirm that if (included in image), then this result reduces to the above one.

a) Now consider another function g(x) expanded in the above basis as (inluded in image). Prove that (in image) b) Now consider a non-orthonormal basis {Xn} for this space, such (included in image) Generalise the previous result to find an expression for (f|g) in terms of Snm. Confirm that if (included in image), then this result reduces to the above one.

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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