DedekindEta

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

Dedekind eta function η(τ), Im(τ) > 0.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaDedekind eta function↗MathWorldDedekindEtaFunction↗WikidataQ1182161↗nLabDedekind eta function↗DLMF23.15↗27.14.E12↗FungrimDedekindEta✓↗Fungrim entryWolfram LanguageDedekindEta✓↗

DedekindEta(complex | infinity) -> numberDedekind eta function η(τ), Im(τ) > 0.

mpmatheta(complex | infinity)Juliaenumeratio_ball(dedekind_eta, complex | infinity)

Typed signatures

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

Domain: Compute engine

Plot

the complex plot cannot lower DedekindEta

Examples

1 more kept as data, checked against the oracles

Basic #

$\eta(i) = \Gamma(1/4) / (2\pi^{3/4})$ numerically

live ↗

In$N(\mathrm{DedekindEta}(i), 15)$Out$0.768\,225\,422\,326\,057$

Known value · mpmath 1.3.0 eta

Scope #

live ↗

In$N(\mathrm{DedekindEta}(\frac{12}{5}+i), 50)$Out$0.624\,107\,533\,298\,226\,658\,997\,763\,691\,379\,683\,078\,838\,230\,308\,461\,63+0.452\,399\,556\,329\,772\,489\,839\,907\,262\,916\,401\,475\,754\,798\,637\,183\,17i$

Applications #

live ↗

In$N((2π)^{12}\mathrm{DedekindEta}(i)^{24})$Out$6\,759\,064.906\,012\,784\,704\,164\,554\,826\,167\,169\,398\,071\,173\,12$

Properties #

live ↗

In$N(\mathrm{DedekindEta}(i+10^{22}), 20)$Out$-0.384\,112\,711\,163\,028\,329\,5-0.665\,302\,731\,567\,394\,126\,21i$

About

Examples	5
Checked against	Wolfram Language 5 agreempmath 4 agree1 differJulia 5 agree
Crosswalk	WikipediaMathWorldWikidatanLabDLMF ×2FungrimFungrim entry ×34Wolfram LanguagempmathJulia

Implementation

mappedmpmathpackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts