6 CONTENTS 4.2.3 Special Comparison Test 309 4.3 Conditional Convergence 4.3.1 Test for Conditional Convergence 4.3.2 Absolute v.s. Conditional 317 4.4 Power Series 320 4.4.1 Radius of Convergence 322 4.4.2 Function Defined by Power Series 325 4.5 Fourier Series 328 4.5.1 Fourier Coefficient 329 4.5.2 Complex Form of Fourier Series 4.5.3 Derivative and Integration of Fourier Series 336 4.5.4 Sum of Fourier Series 339 4.5.5 Parseval's Identity6 CONTENTS 4.2.3 Special Comparison Test . . . . . . . . . . . . . . . . . . . . . 309 4.3 Conditional Convergence . . . . . . . . . . . . . . . . . . . . . . . . . 313 4.3.1 Test for Conditional Convergence . . . . . . . . . . . . . . . . 314 4.3.2 Absolute v.s. Conditional . . . . . . . . . . . . . . . . . . . . 317 4.4 Power Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 4.4.1 Radius of Convergence . . . . . . . . . . . . . . . . . . . . . . 322 4.4.2 Function Defined by Power Series . . . . . . . . . . . . . . . . 325 4.5 Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 4.5.1 Fourier Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 329 4.5.2 Complex Form of Fourier Series . . . . . . . . . . . . . . . . . 334 4.5.3 Derivative and Integration of Fourier Series . . . . . . . . . . . 336 4.5.4 Sum of Fourier Series . . . . . . . . . . . . . . . . . . . . . . . 339 4.5.5 Parseval’s Identity . . . . . . . . . . . . . . . . . . . . . . . . 341