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Stirling's formula Baby Rudin
analysis
logarithms
exponential-function
gamma-function
change-of-variable
Baby rudin 8.21
analysis
trigonometry
gamma-function
change-of-variable
beta-function
How can this integral expression for the difference between two $\zeta(s)$s be explained?
number-theory
gamma-function
riemann-zeta
mellin-transform
Estimate $\displaystyle\int_0^\infty\frac{t^n}{n!}e^{-e^t}dt$ accurately.
asymptotics
power-series
gamma-function
The Laurent series of the digamma function at the negative integers
complex-analysis
special-functions
gamma-function
laurent-series
How to evaluate this nonelementary integral?
multivariable-calculus
gamma-function
Airy function value and derivative value at 0
integration
contour-integration
gamma-function
airy-functions
Integral of squared lower incomplete gamma function
integration
gamma-function
Expand the incomplete gamma function $\int_0^x e^{-t}t^n dt$
sequences-and-series
gamma-function
What does the factorial of a negative number signify?
permutations
factorial
gamma-function
How to Integrate $ \int^{\pi/2}_{0} x \ln(\cos x) \sqrt{\tan x}\,dx$
calculus
integration
definite-integrals
gamma-function
beta-function
Solving $\int_0^{\frac{\pi}{2}}\frac{1}{\sin^{2n}(x) + \cos^{2n}(x)}\:dx$
integration
definite-integrals
gamma-function
trigonometric-integrals
beta-function
Need help with substitution for an integral
gamma-function
Question about a function that is a ratio of gamma functions and appears to be strictly increasing for $x\ge 2$
derivatives
gamma-function
How to express the Riemann hypothesis in terms of the Gamma function?
gamma-function
riemann-hypothesis
How to prove asymptotic limit of an incomplete Gamma function
limits
special-functions
gamma-function
Integrals related to $\int_0^{\pi} \left(\frac{\sin(\alpha u)^\alpha \sin((1-\alpha) u)^{1-\alpha}}{\sin u} \right)^{\rho/\alpha}du$
integration
complex-analysis
probability-distributions
gamma-function
beta-function
A $\log$ integral with a parameter
calculus
sequences-and-series
integration
improper-integrals
gamma-function
Trigamma identity $4\,\psi_1\!\left(\frac15\right)+\psi_1\!\left(\frac25\right)-\psi_1\!\left(\frac1{10}\right)=\frac{4\pi^2}{\phi\,\sqrt5}.$
calculus
special-functions
gamma-function
conjectures
polygamma
Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$
sequences-and-series
closed-form
gamma-function
hypergeometric-function
elliptic-integrals
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