Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Textbook Question

Chapter 12.5, Problem 2P

Verify (5.5) using (5.1).

(5.1) Φ ( x , h ) = 1 − 2 x h + h 2 − 1 / 2 , | h | < 1 ,

(5.5) 1 − x 2 ∂ 2 Φ ∂ x 2 − 2 x ∂ Φ ∂ x + h ∂ 2 ∂ h 2 ( h Φ ) = 0 .

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Chapter 12.5, Problem 1P

Chapter 12.5, Problem 3P

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Mathematical Methods in the Physical Sciences

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Verify (5.5) using (5.1). (5.1) Φ ( x , h ) = 1 − 2 x h + h 2 − 1 / 2 , | h | &lt; 1 , (5.5) 1 − x 2 ∂ 2 Φ ∂ x 2 − 2 x ∂ Φ ∂ x + h ∂ 2 ∂ h 2 ( h Φ ) = 0 .

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Verify (5.5) using (5.1). (5.1) Φ ( x , h ) = 1 − 2 x h + h 2 − 1 / 2 , | h | < 1 , (5.5) 1 − x 2 ∂ 2 Φ ∂ x 2 − 2 x ∂ Φ ∂ x + h ∂ 2 ∂ h 2 ( h Φ ) = 0 .