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Is there a neat way to show $\int_{-1}^1 \frac{ U_n(z) U_n(z)}{\sqrt{1-z^2}} \mathrm{d} z = \pi (n+1)$

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#integration #polynomials #special-functions #orthogonal-polynomials
437
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orthonormal polynomials

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#polynomials #special-functions
1.4k
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Conceptually, what is the difference between the Beta function and the Beta distribution?

Published on
#calculus #probability-distributions #special-functions
254
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please help with the a gamma function since i don't even have the idea?

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#complex-analysis #special-functions #gamma-function
4.2k
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Logarithmic derivative of Riemann Zeta function

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#special-functions #analytic-number-theory #riemann-zeta
898
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Digamma function integral

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#calculus #integration #special-functions
2k
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the limit of the ratio of two $\Gamma(x)$ functions

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#special-functions #asymptotics #gamma-function
1.7k
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Is there a combinatorial way to see the link between the beta and gamma functions?

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#combinatorics #special-functions #binomial-coefficients #gamma-function
186
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Solving for $y$ in $y = x \ln(y)$

Published on
#special-functions #logarithms
118
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Computing the PDF of a product of the sum of 2 Nakagmi-m R.V.s with a Normal R.V

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#sequences-and-series #probability-distributions #special-functions
733
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Intriguing polynomials coming from a combinatorial physics problem

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#combinatorics #polynomials #special-functions #q-analogs
3.1k
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Inverse of the polylogarithm

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#logarithms #special-functions #inverse-function #polylogarithm
464
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Nested Integral of exponential function with trigonometric identities

Published on
#integration #special-functions #normal-distribution
123
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Integrating a differential equation?

Published on
#calculus #ordinary-differential-equations #special-functions #integration
63
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Further simplifiable?

Published on
#ordinary-differential-equations #special-functions #eigenvalues-eigenvectors

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