LogIntegral

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Logarithmic integral li(x) = PV ∫₀ˣ dt/ln t = Ei(ln x).

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaLogarithmic integral function↗MathWorldLogarithmicIntegral↗WikidataQ1350206↗nLablogarithmic integral function↗FungrimLogIntegral↗Wolfram LanguageLogIntegral✓↗

LogIntegral(complex | infinity) -> numberAs native, and keeps its digits past a double's for positive real argument (N(LogIntegral(2), 50)).

SageMathlog_integral(complex | infinity)mpmathli(complex | infinity)Juliaenumeratio_ball(log_integral, complex | infinity)

Typed signatures

Type	Package	Applies
(complex | infinity) -> number	analyticreplaces compute-engine	always
(complex | infinity) -> number	compute-engine	always

Domain: Compute engine

Plot

ComplexPlot

real slice

Examples

Basic #

live ↗

In$\operatorname{li}(0)$Out$0$

live ↗

In$N(\operatorname{li}(2))$Out$1.045\,163\,780\,117\,492\,7$

Known value · mpmath 1.3.0 li

Scope #

live ↗

In$N(\operatorname{li}(2), 50)$Out$1.045\,163\,780\,117\,492\,784\,844\,588\,889\,194\,613\,136\,522\,615\,578\,151\,2$

live ↗

In$\operatorname{li}(1)$Out$-∞$

live ↗

In$\operatorname{li}(∞)$Out$∞$

live ↗

In$\frac{\mathrm{d}\operatorname{li}(x)}{\mathrm{d}x}$Out$\frac{1}{\ln(x)}$

live ↗

In$\operatorname{Series}(\operatorname{li}(x), x, 2, 3)$Out$\operatorname{li}(2)+\frac{x-2}{\ln(2)}-\frac{(x-2)^2}{4\ln(2)^2}+\frac{(2\ln(2)+\ln(2)^2)(x-2)^3}{24\ln(2)^4}+O\left((x-2)^4\right)$

About

Examples	7
Checked against	Wolfram Language 7 agreeSageMath 7 agreempmath 5 agreeJulia 3 agree2 error
Crosswalk	WikipediaMathWorldWikidatanLabFungrimWolfram LanguageSageMathmpmathJulia

Implementation

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts