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12.1.1 From the product of the generating functions g(x, t) g(x, -t) show that 1 = [Jo(x)]²+ 2[J₁(x)]² + 2[J₂(x)]² +…... and therefore that | Jo(x)| ≤ 1 and Jn(x)| ≤ 1/√2, n = 1, 2, 3, .... Hint. Use uniqueness of power series (Section 5.7).

12.1.1 From the product of the generating functions g(x, t) g(x, -t) show that 1 = [Jo(x)]²+ 2[J₁(x)]² + 2[J₂(x)]² +…... and therefore that | Jo(x)| ≤ 1 and Jn(x)| ≤ 1/√2, n = 1, 2, 3, .... Hint. Use uniqueness of power series (Section 5.7).

Advanced Engineering Mathematics
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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12.1.1 From the product of the generating functions g(x, t) g(x, -t) show that 1 = [Jo(x)]²+ 2[J1₁(x)]² + 2[J₂(x)]²+... and therefore that Jo(x)| ≤ 1 and Jn(x)| ≤ 1/√√2, n = 1, 2, 3, .... Hint. Use uniqueness of power series (Section 5.7).
Transcribed Image Text:12.1.1 From the product of the generating functions g(x, t) g(x, -t) show that 1 = [Jo(x)]²+ 2[J1₁(x)]² + 2[J₂(x)]²+... and therefore that Jo(x)| ≤ 1 and Jn(x)| ≤ 1/√√2, n = 1, 2, 3, .... Hint. Use uniqueness of power series (Section 5.7).
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