IncompleteEllipticF

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

Wolfram's own EllipticF, mapped through for the transpiler and the oracle but not yet written up here.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimIncompleteEllipticF✓↗Fungrim entryWolfram LanguageEllipticF!↗

IncompleteEllipticF(...)Wolfram's own EllipticF, mapped through for the transpiler and the oracle but not yet written up here.

Typed signatures

Type	Package	Applies
(number, number) -> number	analytic	always

Domain: Wolfram

Plot

Examples

13 more kept as data, checked against the oracles

Basic #

F(0,m) = 0 for any m, trivially — the integral's upper limit is its lower limit.

live ↗

In$\mathrm{IncompleteEllipticF}(\mathrm{JacobiAmplitude}(0, 0), 0)$Out$0$

Known value · Wolfram MathematicalFunctionData, EllipticF

Same identity at m = 1.

live ↗

In$\mathrm{IncompleteEllipticF}(\mathrm{JacobiAmplitude}(0, 1), 1)$Out$0$

Known value · Wolfram MathematicalFunctionData, EllipticF

Possible issues #

arccsc(0) is ComplexInfinity; stays symbolic here — Wolfram's own EllipticF[ArcCsc[0],0] answers Indeterminate (shown as NaN).

live ↗

In$\mathrm{IncompleteEllipticF}(\mathrm{arccsc}(0), 0)$Out$\mathrm{EllipticF}(\tilde∞, 0)$

Same as above, shifted by π: arccsc(0) still dominates and the result stays symbolic.

live ↗

In$\mathrm{IncompleteEllipticF}(π+\mathrm{arccsc}(0), 0)$Out$\mathrm{EllipticF}(\tilde∞, 0)$

About

Examples	17
Checked against	Wolfram Language 15 agree2 differSageMath 15 agree2 differSymPy 13 agree2 differmpmath 13 agree2 error
Crosswalk	FungrimFungrim entry ×19Wolfram LanguageSageMathSymPympmath

Implementation

mappedsympypackages/oracle/src/mappings.ts

The second argument is the parameter m = k^2 in both, not the modulus k.

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts