1.9 Fourier Integral

1.9 Fourier Integral

• The representation of a periodic function with the same period was developed in Sections 1 and 2.
• We obtained series representations for functions only on a finite interval.
• Some changes suggest an answer.

• We modify Eq.
• now.

• The foregoing derivation is not a proof.

• The two examples show that one can't evaluate the integral in the representation.
• The equality between a suitable function and its Fourier integral is stated in the preceding.

• Section 1.5 for Fourier series contains rules for operations on Fourier integrals.

• Find a rationale for saying that this function can be represented by its integral Fourier.