Any pair of equations giving the Real Part of a function as an integral of its Imaginary Part and the
Imaginary Part as an integral of its Real Part. Dispersion relationships imply causality in physics. Let

(1) |

(2) | |||

(3) |

where denotes the Cauchy Principal Value and and are Hilbert Transforms of each other. If the Complex function is symmetric such that , then

(4) | |||

(5) |

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