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DedekindEta

DedekindEta[]
gives the Dedekind eta modular elliptic function .
  • 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.
Evaluate numerically:
Evaluate numerically:
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Evaluate to high precision:
The precision of the output tracks the precision of the input:
DedekindEta threads element-wise over lists:
TraditionalForm formatting:
Plot the DedekindEta in the upper-half complex plane:
The modular discriminant:
Relation with DedekindEta:
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:
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