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How to evaluate this integral without numerical methods?

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#integration #definite-integrals #hypergeometric-function #digamma-function
217
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Limit involving gamma and digamma function

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#sequences-and-series #gamma-function #digamma-function
178
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A property of the _digamma_ function

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#divergent-series #digamma-function
137
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What about $\sum_{n=1}^\infty\frac{\mu(n)}{n}\psi\left(1+\frac{1}{n}\right)$ as $\frac{1}{2}$?

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#real-analysis #sequences-and-series #analytic-number-theory #mobius-function #digamma-function
251
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Simultaneous transcendental equations involving digamma functions.

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#systems-of-equations #special-functions #transcendental-equations #digamma-function
92
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Integrating $\psi'$ to get $\Gamma$

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#calculus #special-functions #gamma-function #digamma-function
63
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Partial sum formula for $\sum_{x=1}^n \frac{1}{bx - x^2}$ at specific limit without using digamma function

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#summation #harmonic-numbers #digamma-function
48
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Computing $\lim_{\varepsilon\to 0^{+}}\psi(\varepsilon)/\Gamma(\varepsilon)$ with asymptotic expansions

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#limits #asymptotics #gamma-function #limits-without-lhopital #digamma-function
145
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Ratio of hypergeometric function with a "Harmonic twist" to a hypergeometric function

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#calculus #summation #gamma-function #hypergeometric-function #digamma-function
79
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Tricky partial rational sum

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#summation #harmonic-numbers #digamma-function
225
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Proof trigamma recurrence relation

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#calculus #recurrence-relations #gamma-function #digamma-function
128
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Evaluate $\int_{0}^{\infty}e^{-x^2}\ln(x)dx$

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#calculus #integration #gamma-function #digamma-function
167
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Taylor series with logarithmic coefficients

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#convergence-divergence #logarithms #taylor-expansion #generating-functions #digamma-function
121
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Digamma function and asymptotic bounds

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#asymptotics #wolfram-alpha #digamma-function
781
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How to calculate $\int_0^{\frac{\pi}{2}}{x^2\cot x\ln\cos x\, \text{d}x}$.

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#calculus #integration #definite-integrals #harmonic-numbers #digamma-function

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