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The American Mathematical Monthly Volume 121, 2014 - Issue 3
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The Weighted Hermite Polynomials Form a Basis for L2(ℝ)

William JohnstonDepartment of Mathematics & Actuarial Science, Butler University, Indianapolis, [email protected]
Pages 249-253 | Published online: 13 Dec 2017
 
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Abstract

We present a student-friendly proof that the weighted Hermite polynomials form a complete orthonormal system (a basis) for the collection L2(ℝ) of real-valued functions.

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