Question

Find the Fourier series expansion of f(x) = e^ax in the interval (0,2π).​

Answer 1

Answer:

We know, x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

= 1/2(x + y + z )[2x² + 2y² + 2z² - 2xy - 2yz - 2zx]

= 1/2(x + y + z) [x² + x² + y² + y² + z² + z² - 2xy - 2yz - 2zx ]

= 1/2 (x + y + z) [ x² + y² - 2xy + y² + z² - 2yz + z² + x² - 2zx ]

= 1/2(x + y + z) [(x² + y² - 2xy) + (y² + z² - 2yz) + (z² + x² - 2zx)]

= 1/2(x + y + z) [ (x - y)² + (y - z)² + (z - x)² ]

Hence, x³ + y³ + z³ - 3xyz = 1/2(x + y + z) [ (x - y)² + (y - z)² + (z - x)² ]

Answer 2

Answer:

Find the Fourier series expansion of f(x) = e^ax in the interval (0,2π).