The Main Theorem
The Main Theorem : Statement : If a function f is bounded periodic with period 2π and integrable on [-π,π] , and piecewise monotonic on [-π,π], then ∞ 1/2 a₀ + Σ (aₙcosnξ + bₙsinnξ) n=1 [1/2 [f(ξ-)+f(ξ+)], for -π<ξ<π , = [1/2 [f(π-)+f(-π+)] , for ξ= ±π where aₙ , bₙ are Fourier coefficients of f. Proof : ∞ Let 1/2 a₀+Σ (aₙcosnx +bₙsinnx) be n=1 the Fourier Series of f ,...