Some Transformation Properties of the Incomplete Beta Function and Its Partial Derivatives

In this paper, some transformation properties of the incomplete Beta function B(z; x, y) are obtained. Based on the transformation properties, we extend the definitions of the partial derivatives of the incomplete Beta function Bp,q(z; x, y) to the whole complex plane on x, y and z. Furthermore, we...

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Published in:IAENG international journal of applied mathematics 2019-02, Vol.49 (1), p.1-5
Main Authors: Li, Aijuan, Qin, Huizeng
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Language:English
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Complex numbers
Derivatives
Economic models
Properties (attributes)
Transformations
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description In this paper, some transformation properties of the incomplete Beta function B(z; x, y) are obtained. Based on the transformation properties, we extend the definitions of the partial derivatives of the incomplete Beta function Bp,q(z; x, y) to the whole complex plane on x, y and z. Furthermore, we give some representations of Bp,q(z; x, y) for complex numbers x, y, z. Moreover, numerical examples show the transformation formulas can improve the speed and precision of calculating B(z; x,y) and Bp,q(z; x,y).
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subjects Complex numbers
Derivatives
Economic models
Properties (attributes)
Transformations
title Some Transformation Properties of the Incomplete Beta Function and Its Partial Derivatives
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