# Tagged Questions

For questions that involve concrete approximations, such as finding an approximate value of a number with some precision. For questions that belong to the mathematical area of Approximation Theory, use (approximation-theory).

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### Approximation of a quotient that involves the Lambert function.

I would like to find an asymptotic upper bound for $$\frac{-\ln n}{W(- \ln^{-c}n)}$$ where $c$ is positive and $W$ is the Lambert function. More precisely, I want something which dominates this ...
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### Upper bound on the remainder of a polynomial (not taylor)

There are many ways of approximating a function with a polynomial, $\widehat{f}(x)\approx f(x)$. One way is the taylor polynomial. A nice property that goes along with the taylor polynomial is an ...
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### Approximate roots of nonlinear equation (non-integer polynomial)

In case of pulsating bubble arising from underwater explosion, bubble radius satisfies the following equation. $x^3\dot{x}^{2} + x^3 + \frac{k}{x^{3(\gamma-1)}} = 1$ The minimum and maximum bubble ...
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### What's the most accurate way to estimate a percentile from multiple partial percentiles?

There exists 3 sets of numbers. I have the 99th percentile (p99) of each set and the cardinality of the set, but not the values in the set themselves. p99: 540, cardinality: 215 p99: 288, ...
### Upper bound on ratio of incomplete Gamma function and Gamma function $\frac{ \Gamma \left( x; a\right)}{\Gamma(x)}$
I am trying to find a tight upper bound the following expression \begin{align} \frac{ \Gamma \left( x; a\right)}{\Gamma(x)} \end{align} where $\Gamma \left( x; a\right)$ is incomplet Gamma function \...