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New posts in special-functions
Yet another difficult logarithmic integral
integration
sequences-and-series
special-functions
hypergeometric-function
polylogarithm
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
complex-analysis
integration
special-functions
Integral $\int_0^\infty \frac{\cos x}{x}\left(\int_0^x \frac{\sin t}{t}dt\right)^2dx=-\frac{7}{6}\zeta(3)$
real-analysis
integration
complex-analysis
definite-integrals
special-functions
Closed form of $\int e^{i\csc^2(x)}dx=\int \cos\left(\csc^2(x)\right)dx+i\int \sin\left(\csc^2(x)\right)dx$
special-functions
closed-form
hypergeometric-function
trigonometric-integrals
fresnel-integrals
Contour integral representation of Confluent Hypergeometric Function
complex-analysis
special-functions
contour-integration
Closed form of an improper integral to solve the period of a dynamical system
integration
improper-integrals
special-functions
lambert-w
elliptic-integrals
Evaluate $\int _{ }^{ }\frac{1}{\sqrt{1+x^3}}dx$
calculus
integration
indefinite-integrals
special-functions
hypergeometric-function
Recursive solutions to linear ODE.
ordinary-differential-equations
special-functions
Does this integral have a closed form: $\int_0^1 \frac{x^{\beta-1}}{1-x}\log\frac{1-y x^\delta}{1-y}\mathrm dx$?
sequences-and-series
integration
special-functions
definite-integrals
Integral of binomial coefficients
integration
special-functions
gamma-function
bernoulli-numbers
pochhammer-symbol
tough integral involving the Cosine integral
calculus
integration
special-functions
Show the equivalence of two infinite series over Bessel functions
sequences-and-series
special-functions
bessel-functions
Derivative of the elliptic integral of the first kind
calculus
special-functions
elliptic-integrals
Closed-form of log gamma integral $\int_0^z\ln\Gamma(t)~dt$ for $z =1,\frac12, \frac13, \frac14, \frac16,$ using Catalan's and Gieseking's constant?
definite-integrals
logarithms
special-functions
closed-form
gamma-function
Is there a precise mathematical connection between hypergeometric functions and modular forms
special-functions
modular-forms
Did Euler have an alpha function?
special-functions
math-history
Simplification of a trilogarithm of a complex argument
calculus
complex-analysis
complex-numbers
special-functions
polylogarithm
Simplify $\Gamma\left(\frac27\right) \Gamma\left(\frac{11}{42}\right)/\;\Gamma\left(\frac1{21}\right)$ to elementary terms
calculus
trigonometry
special-functions
gamma-function
Evaluating $\int_0^1 \frac{\text{Li}_2 \left(-\frac{1}{1-z}\right)-\text{Li}_2 \left(-\frac{1}{1+z}\right)}{z}dz$
definite-integrals
special-functions
closed-form
Integral $\int\limits_0^\infty \prod\limits_{k=0}^\infty\frac{1+\frac{x^2}{(b+1+k)^2}}{1+\frac{x^2}{(a+k)^2}} \ dx$
calculus
integration
special-functions
improper-integrals
gamma-function
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