Engineering Mathematics: Polylogarithm

Showing posts with label Polylogarithm. Show all posts

Showing posts with label Polylogarithm. Show all posts

Monday, February 11, 2013

Polylogarithm

Definition of Polylogarithm

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PL.ID.1: Functional Equation of Polylogarithm

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Proof

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

(1)

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(2)

summing (1) and (2)

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This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

(3)

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

(4)

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

(5)

using the definition of polylogarithm , the function equation is:

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Friday, June 1, 2012

Gamma-Polylogarithm

GP.ID.1:

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Proof

Given

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(1)

therefore ,

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(2)

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(3)

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

(4)

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

(5)

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(6)

Based on the identity:

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(7)

From (5) and (6) ,

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