BesselI

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

Modified Bessel function of the first kind

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaModified Bessel function↗WikidataQ2607225↗DLMF10.25.E2↗FungrimBesselI✓↗Fungrim entryWolfram LanguageBesselI✓↗

BesselI(order: complex, complex | infinity) -> numberAs native, and keeps its digits past a double's for integer order and real argument (N(BesselI(1, 1), 40)).

SageMathbessel_I(order: complex, complex | infinity)SymPybesseli(order: complex, complex | infinity)mpmathbesseli(order: complex, complex | infinity)Juliaenumeratio_ball(bessel_i, order: complex, complex | infinity)

Typed signatures

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

Domain: Compute engine

Plot

ComplexPlot

real slice

Examples

Basic #

live ↗

In$N(\operatorname{I}_{0}(1))$Out$1.266\,065\,877\,752\,008\,4$

Known value · mpmath 1.3.0 besseli

live ↗

In$\operatorname{Normal}(\operatorname{Series}(\operatorname{I}_{0}(x), x, ∞, 2))$Out$(\frac{\sqrt{2}}{16\sqrt{π}\sqrt{x}^{3}}+\frac{1}{\sqrt{x}\sqrt{2π}})e^{x}+(\frac{-\frac{\sqrt{2}}{16}i}{\sqrt{π}\sqrt{x}^{3}}+\frac{\frac{\sqrt{2}}{2}i}{\sqrt{π}\sqrt{x}})e^{-x}$

Scope #

live ↗

In$N(\operatorname{I}_{0}(1), 50)$Out$1.266\,065\,877\,752\,008\,335\,598\,244\,625\,214\,717\,537\,607\,670\,311\,355$

About

Examples	3
Checked against	Wolfram Language 3 agreeSageMath 2 agree1 unevaluatedSymPy 2 agree1 unevaluatedmpmath 2 agreeJulia 2 agree
Crosswalk	WikipediaWikidataDLMFFungrimFungrim entry ×14Wolfram LanguageSageMathSymPympmathJulia

Implementation

mappedsympypackages/oracle/src/mappings.ts

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts