Monday Math 44

Now that we know how to find the derivatives of the gamma function, we can also find the partial derivatives of the beta function. We know that
We see from the symmetry between x and y that

Finding the second partial derivatives, we see first that

So we just need the mixed partial derivative

These have a number of applications to definite integrals involving logarithms.


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One Response to “Monday Math 44”

  1. Monday Math 45 « Twisted One 151’s Weblog Says:

    […] Math 45 As we noted previously, the derivatives of the beta function can be used in solving various integration problems. First, […]

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