SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Mathematica > Mathematics and Algorithms > Mathematical Functions > Number Theoretic Functions >

Built-in Mathematica Symbol

Tutorials »|See Also »|More About »

DedekindEta

DedekindEta[

]
gives the Dedekind eta modular elliptic function

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

DedekindEta is defined only in the upper half of the complex plane. It is not defined for real .

The argument is the ratio of Weierstrass half-periods .

DedekindEta satisfies where is the discriminant, given in terms of Weierstrass invariants by .

For certain special arguments, DedekindEta automatically evaluates to exact values.

DedekindEta can be evaluated to arbitrary numerical precision.

DedekindEta automatically threads over lists.

EXAMPLES

CLOSE ALL

Basic Examples (2)

Evaluate numerically:

Scope (4)

Evaluate to high precision:

The precision of the output tracks the precision of the input:

DedekindEta threads element-wise over lists:

TraditionalForm formatting:

Applications (2)

Plot the DedekindEta in the upper-half complex plane:

The modular discriminant:

Relation with DedekindEta:

Properties & Relations (2)

Machine-precision input is insufficient to give a correct answer:

With exact input, the answer is correct:

Because DedekindEta is a numerical function with numeric arguments, it might be considered a numeric quantity but because of its boundary of analyticity, it might not be evaluatable to a number: