Engineering Mathematics I by Sergei Silvestrov & Milica Rančić

Author:Sergei Silvestrov & Milica Rančić
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Proof

This theorem follows from integration being linear and Lemma 10.4.

Theorem 10.3

For the integral of the AEF is

(10.11)

where is defined as in Lemma 10.4.

When and the integral becomes

(10.12)

where

with

is the Gamma function [1].

Proof

This theorem follows from integration being linear and Lemma 10.4.

In the next section we will estimate the parameters of the AEF that gives the best fit with respect to some data and for this the partial derivatives with respect to the parameters will be useful. Since the AEF is a linear function of elementary functions these partial derivatives can easily be found using standard methods.

Theorem 10.4

The partial derivatives of the p-peak AEF with respect to the parameters are

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