List questions from lambert-w

Published on 05 Mar 2023 - 21:02

106

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Show that $x/e^x<1.5/x^2$ for $x>0$

Published on 05 Mar 2023 - 21:47

153

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Is the Lambert W function the Newton flow of the exponential function?

Published on 23 Feb 2026 - 11:53

238

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Evaluate the definite integral $\int_0^\infty \frac{W{(x)}}{xe^x}\,dx$

Published on 26 Mar 2026 - 2:55

147

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How to rewrite $e^{-x} = -\ln(x)$ such that the Lambert W function can be applied?

Published on 14 Apr 2023 - 15:31

83

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On combinatoric equality $\sum_{i=1}^{n-1}{n\choose i} i^{i-1} (n-i)^{n-i-1}=2(n-1)n^{n-2}$

Published on 04 May 2023 - 9:08

117

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Showing that $\ln(x)^2+2(x-1)\ln x-3x+1=0$ has only $2$ real solutions

Published on 09 May 2023 - 16:25

79

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Solving $B a^t + C a^{2t} + D t a^t + E t^2 + F t + G = 0$

Published on 15 May 2023 - 12:29

137

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How to solve $a \cdot x^{2} + b \cdot x + c + \exp\left( d \cdot x + e \right) = 0$ for $x$ where $x \in \mathbb{C} \cup \{ \hat{\infty} \}$?

Published on 19 May 2023 - 22:41

84

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Reference books on Lambert function

Published on 24 May 2023 - 3:22

117

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Upper bound on the Lambert function

Published on 25 May 2023 - 13:29

84

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If $1 < x < e < y$ and $x^{1/x} = y^{1/y}$ then $y > e^2/x$.

Published on 10 Jun 2023 - 20:48

62

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Evaluate $\sum\limits_{n=0}^\infty\operatorname W(e^{e^{an}})x^n$ with Lambert W function

Published on 21 Jun 2023 - 23:54

239

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How to solve $x + 3^{x} = 4$ using Lambert W Function.

Published on 22 Jun 2023 - 9:31

46

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Approximations and limits for Lambert $W$ of decreasing functions

Published on 24 Jun 2023 - 22:19

List Question

How to solve $x^{y^z}=z$

Show that $x/e^x<1.5/x^2$ for $x>0$

Is the Lambert W function the Newton flow of the exponential function?

Evaluate the definite integral $\int_0^\infty \frac{W{(x)}}{xe^x}\,dx$

How to rewrite $e^{-x} = -\ln(x)$ such that the Lambert W function can be applied?

On combinatoric equality $\sum_{i=1}^{n-1}{n\choose i} i^{i-1} (n-i)^{n-i-1}=2(n-1)n^{n-2}$

Showing that $\ln(x)^2+2(x-1)\ln x-3x+1=0$ has only $2$ real solutions

Solving $B a^t + C a^{2t} + D t a^t + E t^2 + F t + G = 0$

How to solve $a \cdot x^{2} + b \cdot x + c + \exp\left( d \cdot x + e \right) = 0$ for $x$ where $x \in \mathbb{C} \cup \{ \hat{\infty} \}$?

Reference books on Lambert function

Upper bound on the Lambert function

If $1 < x < e < y$ and $x^{1/x} = y^{1/y}$ then $y > e^2/x$.

Evaluate $\sum\limits_{n=0}^\infty\operatorname W(e^{e^{an}})x^n$ with Lambert W function

How to solve $x + 3^{x} = 4$ using Lambert W Function.

Approximations and limits for Lambert $W$ of decreasing functions

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