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The series $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n-1}\mbox{sech}\left(\frac{(2n-1)\pi}{2}\right)$

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#sequences-and-series #complex-analysis #analysis #special-functions
3.1k
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Show that Bessel function $J_n(x)$ satisfies Bessel's differential equation.

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#ordinary-differential-equations #special-functions
190
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Is there a function $f$ such that $\Gamma (c+x)=\Gamma (c-f\left( x \right) )$?

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#special-functions #functional-equations #gamma-function
229
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Understanding the Gamma Function

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#inequality #special-functions #gamma-function
2.1k
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About the Beta function : $\text{B}\left(\frac{4}{3},\frac{2}{3}\right)$.

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#calculus #integration #improper-integrals #special-functions #gamma-function
893
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Non-normalized sinc function

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#fourier-analysis #special-functions
174
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Useful approximation of the pdf

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#multivariable-calculus #probability-distributions #special-functions #approximation
759
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Infinite series of Hypergeometric function

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#sequences-and-series #special-functions #hypergeometric-function
95
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Realization of Bessel functions

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#special-functions
123
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Closed form formula for a double series related to wave equation

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#sequences-and-series #complex-analysis #analysis #partial-differential-equations #special-functions
63
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Sup and lim sup of a function defined by double series

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#sequences-and-series #analysis #partial-differential-equations #special-functions
490
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Prove an identity involving Gamma function and Gaussian hypergeometric function

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#special-functions #gamma-function #hypergeometric-function
3.1k
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Circumference of a superellipse?

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#integration #special-functions #algebraic-curves #plane-curves
935
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Integral of the modified Bessel function of the first kind zero order

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#calculus #integration #special-functions
2.4k
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Integral of the modified Bessel function of the first kind zero order involving power and exponential functions

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#calculus #integration #special-functions

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