ExpIntegralEi

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

Exponential integral Ei(x) = PV ∫_{−∞}^x eᵗ/t dt.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaExponential integral↗MathWorldExponentialIntegral↗WikidataQ1419948↗Encyclopedia of MathematicsIntegral_exponential_function↗DLMF6.2.E1↗6.2.i.p3↗Wolfram LanguageExpIntegralEi!↗

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

SageMathexp_integral_ei(complex | infinity)mpmathei(complex | infinity)Juliaenumeratio_ball(exp_integral_ei, 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 #

A logarithmic singularity at $0$

live ↗

In$\mathrm{ExpIntegralEi}(0)$Out$-∞$

live ↗

In$N(\mathrm{ExpIntegralEi}(1))$Out$1.895\,117\,816\,355\,937$

Known value · mpmath 1.3.0 ei

live ↗

In$\operatorname{Normal}(\operatorname{Series}(\mathrm{ExpIntegralEi}(x), x, ∞, 6))$Out$\frac{1}{2}(2\ln(x)-\ln(-x)+\ln(-\frac{1}{x}))+(\frac{2}{x^3}+\frac{6}{x^4}+\frac{24}{x^5}+\frac{120}{x^6}+\frac{1}{x}+\frac{1}{x^2})e^{x}$

Scope #

live ↗

In$N(\mathrm{ExpIntegralEi}(2), 50)$Out$4.954\,234\,356\,001\,890\,163\,379\,505\,130\,227\,035\,275\,518\,053\,562\,42$

live ↗

In$\mathrm{ExpIntegralEi}(\bigl\lbrack∞, -∞, ∞i, -∞×1i\bigr\rbrack)$Out$\bigl\lbrack∞, 0, \operatorname{Indeterminate}, \operatorname{Indeterminate}\bigr\rbrack$

live ↗

In$\mathrm{ExpIntegralEi}(\tilde∞)$Out$\operatorname{Indeterminate}$

live ↗

In$\frac{\mathrm{d}\mathrm{ExpIntegralEi}(x)}{\mathrm{d}x}$Out$\frac{e^{x}}{x}$

About

Examples	7
Checked against	Wolfram Language 6 agree1 differSageMath 4 agree2 differ1 unevaluatedmpmath 3 agree1 differJulia 2 agree2 error
Crosswalk	WikipediaMathWorldWikidataEncyclopedia of MathematicsDLMF ×2Wolfram LanguageSageMathmpmathJulia

Implementation

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts