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DedekindEta

DedekindEta[

]
gives the Dedekind eta modular elliptic function

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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

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Basic Examples (2)

Evaluate numerically:

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Out[1]=

In[1]:=

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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: