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New posts in gamma-function
A series problem by Knuth
sequences-and-series
approximation
gamma-function
factorial
Prove $\frac{\partial}{\partial m}\text{B}(n,m)=-\text{B}(n,m)\sum_{k=0}^{n-1}\frac{1}{k+m}$
calculus
partial-derivative
gamma-function
harmonic-numbers
beta-function
Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$
integration
complex-analysis
definite-integrals
special-functions
gamma-function
On the general form of the family $\sum_{n=1}^\infty \frac{n^{k}}{e^{2n\pi}-1} $
sequences-and-series
closed-form
gamma-function
bernoulli-numbers
What is the role of mathematical intuition and common sense in questions of irrationality or transcendence of values of special functions?
special-functions
gamma-function
irrational-numbers
philosophy
transcendental-numbers
Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
calculus
integration
definite-integrals
logarithms
gamma-function
Evaluating the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} $
sequences-and-series
complex-analysis
special-functions
binomial-coefficients
gamma-function
Prove that $\frac{1}{\phi}<\int_0^\infty \frac{e^{-x}}{\Gamma(x)} dx< \frac{24+\sqrt{2}}{41} $
inequality
definite-integrals
gamma-function
golden-ratio
a conjectured continued fraction for $\tan\left(\frac{z\pi}{4z+2n}\right)$
number-theory
special-functions
gamma-function
continued-fractions
conjectures
How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$
real-analysis
limits
factorial
closed-form
gamma-function
Why isn't the gamma function defined so that $\Gamma(n) = n! $?
soft-question
special-functions
gamma-function
Çinlar's Probability and Stochastic, Examples 2.11 and 2.12
probability-theory
measure-theory
laplace-transform
gamma-function
Closed form for $\prod_{n=1}^\infty\sqrt[2^n]{\frac{\Gamma(2^n+\frac{1}{2})}{\Gamma(2^n)}}$
calculus
combinatorics
gamma-function
closed-form
infinite-product
How to find the factorial of a fraction?
factorial
gamma-function
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$. [duplicate]
integration
special-functions
improper-integrals
gamma-function
Is it possible to simplify $\frac{\Gamma\left(\frac{1}{10}\right)}{\Gamma\left(\frac{2}{15}\right)\ \Gamma\left(\frac{7}{15}\right)}$?
calculus
special-functions
closed-form
gamma-function
Evaluating the log gamma integral $\int_{0}^{z} \log \Gamma (x) \, \mathrm dx$ in terms of the Hurwitz zeta function
integration
special-functions
gamma-function
riemann-zeta
zeta-functions
An upper bound for the function $x!$ using some well-know constant as $e$ or $\pi$
derivatives
inequality
power-series
gamma-function
constants
Roots of the incomplete gamma function
special-functions
roots
gamma-function
Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$?
analysis
special-functions
gamma-function
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