Equate the coefficients of the quadratic term in the Taylor expansion of cos x to the corresponding coefficient in the infinite product representa- tion of cos x obtained in part (c). Use the result in part (d) above to derive the sum of the reciprocals of the squares of the odd integers: 1+1/9+ 1/25 + 1/49 + 1/81 +···=π^2/8
Equate the coefficients of the quadratic term in the Taylor expansion of cos x to the corresponding coefficient in the infinite product representa- tion of cos x obtained in part (c). Use the result in part (d) above to derive the sum of the reciprocals of the squares of the odd integers: 1+1/9+ 1/25 + 1/49 + 1/81 +···=π^2/8
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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Equate the coefficients of the quadratic term in the Taylor expansion of cos x to the corresponding coefficient in the infinite product representa- tion of cos x obtained in part (c).
Use the result in part (d) above to derive the sum of the reciprocals of the squares of the odd integers:
1+1/9+ 1/25 + 1/49 + 1/81 +···=π^2/8
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