Consider a function space in (-∞, ∞) with orthonormal basis {ˆn}. Show that any functionf(x) expanded in this basis as (equation included in image) has expansion coefficients given by(included in image) Consider a function space in (-∞, ∞) with orthonormal basis {n}. Show that any functionf(x) expanded in this basis as f(x) = En Cnon (r), has expansion coefficients given byCn = (Onlf).

suppose that we express the function is the given format in the question - f(x)= ∑n cnϕn^(x)⇒f(x)=…

Answered: Consider a function space in (-∞0, ∞)…

Consider a function space in (-∞0, ∞) with orthonormal basis {n}. Show that any function f(x) expanded in this basis as f(x) = En Cnon (x), has expansion coefficients given by = (Onlf). Cn =

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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Question

Consider a function space in (-∞, ∞) with orthonormal basis {ˆn}. Show that any function
f(x) expanded in this basis as (equation included in image) has expansion coefficients given by
(included in image)

Consider a function space in (-∞, ∞) with orthonormal basis {n}. Show that any function
f(x) expanded in this basis as f(x) = En Cnon (r), has expansion coefficients given by
Cn = (Onlf).

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