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Hi all,

I am working with some beta functions. I want to show that the following is positive and bounded between 0 and 1. Is it possible to show this?

$$ \frac{ \frac{B( a + b , \frac{2}{ c} )}{B(a, \frac{2}{c}) } - \big\{\frac{B( a + b , \frac{1}{ c} )}{B(a, \frac{1}{c}) }\big\}^{2} }{ \frac{B( a + b , \frac{1}{ c} )}{B(a, \frac{1}{c}) } - \big\{\frac{B( a + b , \frac{1}{ c} )}{B(a, \frac{1}{c}) }\big\}^{2} } $$

where a, b and c are positive real numbers.

Thanks for your help.

Here is a image of the above expression.

I am working with some beta functions. I want to show that the following is positive and bounded between 0 and 1. Is it possible to show this?

$$ \frac{ \frac{B( a + b , \frac{2}{ c} )}{B(a, \frac{2}{c}) } - \big\{\frac{B( a + b , \frac{1}{ c} )}{B(a, \frac{1}{c}) }\big\}^{2} }{ \frac{B( a + b , \frac{1}{ c} )}{B(a, \frac{1}{c}) } - \big\{\frac{B( a + b , \frac{1}{ c} )}{B(a, \frac{1}{c}) }\big\}^{2} } $$

where a, b and c are positive real numbers.

Thanks for your help.

Here is a image of the above expression.

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