Oct 17, 2019 · $$\operatorname {Ei} (x)=\operatorname {Ei} (-1)-\int_ {-x}^1\frac {e^ {-t}}t~\mathrm dt$$ which are both easily differentiated using the fundamental theorem of calculus, now that we have …

Quiz: Spelling- 'ie' or 'ei'? This is a beginner/elementary-level quiz containing 10 multichoice quiz questions from our 'spelling and punctuation' category. Simply answer all questions and press the …

Apr 19, 2024 · This result can be obtained directly from a Maclaurin expansion of the function. By denoting \begin {equation} y=\mathrm {Ei}^ {-1} (x) \end {equation} the integral ...

Sep 23, 2024 · I was trying to calculate the limit $$\lim_ {x\to0}2\text {Ei} (-x)-2\text {Ei} (-2x)$$ and I had absolutely no idea how to do it and how it simplifies to: $$-\ln4$$ This was for the bounds of an …

$\operatorname {Ei} (x)$ is a special function and is generally agreed to be considered useful enough to have it's own place amongst the special functions.

Feb 18, 2013 · Intuition comes from knowledge and experience! Learning facts about complex exponentiation then making use of those facts to solve problems will build your experience.

Oct 13, 2021 · Prove Euler's identity $e^ {i\theta} = \cos \theta + i \sin \theta$ using Taylor series. Then plug in $\theta = \pi$.

Feb 17, 2019 · Having an integral like $\int_ {2}^ {10} {\frac {x} {\ln x}}dx$ How does this function turns to an exponential integral of the form: $ \operatorname {Ei} (x)=-\int ...

Mar 12, 2005 · First, it's not "e.i" it's "i.e." Both "i.e." and "e.g." are from Latin and have different meanings and uses: i.e. = "id est" which means approximately "that is [to say]" Use it to expand …

Oct 19, 2021 · EDIT: I don't know why, but information on the web about the complex function $\operatorname {Ei} (s)$ is very scarce. But it's an important function used a lot in analytic number …