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2h
comment Solution of Integral $\int_0^\infty \frac{x^{r/\beta}e^{-\alpha x}}{\left(1-(1-\beta)e^{-x}\right)^{\alpha+1}} \, dx$
@SAAN Thanks for you great trial. But isn't the first approach in fact suitable for $|1-\beta|<1$ , i.e. $0<\beta<2$ , and the second approach in fact suitable for $|1-\beta|>1$ , i.e. $\beta>2$ ?
2h
comment Some properties about the Kampé de Fériet function
But how to prove $\sum\limits_{s_1,\ldots,s_n=0}\dfrac{\prod\limits_{j=1}^p(a_j)_{s_1+\ldots s_n}}{\prod\limits_{l=1}^q(b_l)_{s_1+\ldots s_n}}\dfrac{x_1^{s_1}}{s_1!}\ldots\dfrac{x_n^{s_n}}{s_n!}=\sum\limits_{k=0}^\inf‌​ty\dfrac{\prod\limits_{j=1}^p(a_j)_{k}}{\prod\limits_{l=1}^q(b_l)_{k}} \dfrac{(x_1+...+x_n)^k}{k!}$ ? Natural is not the reasonable reason in maths!
2h
revised Can anyone solve this integral function?
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3h
answered Infinite series of Hypergeometric function
3h
comment Solution of Integral $\int_0^\infty \frac{x^{r/\beta}e^{-\alpha x}}{\left(1-(1-\beta)e^{-x}\right)^{\alpha+1}} \, dx$
@user64494 But at least she gives the expressable series form, don't you know that the integral is more complicated than Lerch zeta function?
22h
asked Some properties about the Kampé de Fériet function
22h
revised Evaluting $\int_{1}^{2} \frac{\tan^{-1} x}{\tan^{-1} \frac {1}{x^2-3x+3}} \operatorname dx$
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1d
comment Closed form for an infinite sum over Gamma functions?
@Jack D'Aurizio Converting series back to the integral form is not the expected way of simplification.
1d
comment Expressing ${}_2F_1(a, b; c; z)^2$ as a single series
@glebovg at least it relates to the Legendre function in this way: functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1/…
1d
revised Closed form for an infinite sum over Gamma functions?
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1d
revised Closed form for an infinite sum over Gamma functions?
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2d
revised Closed form for an infinite sum over Gamma functions?
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2d
answered Closed form for an infinite sum over Gamma functions?
2d
answered solving the integral of $e^{x^2}$
2d
revised How to prove and evaluate an Improper Integral
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Apr
21
revised How to solve over-determined linear system of equations?
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Apr
21
revised Limit of solution equal to solution at limit
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Apr
21
revised Two variable equation
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Apr
21
revised Find a line parallel to a known line that intersects a known circle at one point.
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Apr
21
revised Question regarding arbitrary parameters
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