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What would you name the $fm(x) = \frac{f(x)}{x}$ pattern?

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#functions #special-functions
123
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Explicit expression for $\int_{0}^{+\infty} dr \,r e^{-\beta r^{2}}I_{0}(\beta r\rho)I_{0}(\beta r a)$

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#integration #definite-integrals #special-functions #bessel-functions
484
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Rodrigues' Formula for Laguerre equation

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#ordinary-differential-equations #polynomials #special-functions #orthogonal-polynomials #laguerre-polynomials
155
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Calculation of integral using Bessel functions

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#integration #analysis #special-functions #bessel-functions
132
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How to estimate the following integral involving exponentials and Bessel functions

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#definite-integrals #asymptotics #special-functions #closed-form #bessel-functions
124
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How do you derive the "reflection formula" for the digamma function?

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#special-functions #digamma-function
372
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Bessel Function Analytic Continuation

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#complex-analysis #special-functions #integers #bessel-functions #analytic-continuation
150
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Estimate of $\int_y^{+∞}\frac{[2-({\rm erf}(x+a)+{\rm erf}(x-a))]^2}{e^{-(x+a)^2}+e^{-(x-a)^2}}\,\mathrm dx$

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#calculus #asymptotics #improper-integrals #special-functions
151
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Simplifying $\sin(a\arcsin(x))$

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#algebra-precalculus #trigonometry #special-functions
129
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Hypergeometric transformations

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#complex-analysis #special-functions #transformation #hypergeometric-function
73
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Inverse of $f(x)=x/\log(1+x)$ for $x>1$

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#special-functions
98
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Explicit formula for a power series asymptotic approximation of $z^u$ given any complex exponent $u$.

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#special-functions #exponentiation #closed-form #residue-calculus #laurent-series
91
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Solving or approximating integral of $e^{-u^2}$ divided by quadratic function

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#calculus #integration #improper-integrals #special-functions
120
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Asymptotic behavior of a Bessel-function-like integral

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#definite-integrals #improper-integrals #special-functions #hyperbolic-functions
182
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Evaluating $\int_0^y \frac{z^2e^{az}}{e^z-1}\,\mathrm dz$.

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#definite-integrals #special-functions #hypergeometric-function #zeta-functions #bernoulli-numbers

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