23 Weierstrass Elliptic and Modular FunctionsModular Functions23.15 Definitions23.17 Elementary Properties

§23.16 Graphics

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Keywords:

graphics, modular functions

Notes:

These graphics were produced at NIST.

Permalink:

http://dlmf.nist.gov/23.16

See also:

Annotations for Ch.23

See Figures 23.16.1–23.16.3 for the modular functions $\lambda$, $J$, and $\eta$. In Figures 23.16.2 and 23.16.3, height corresponds to the absolute value of the function and color to the phase. See also About Color Map.

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Symbols:

$\eta \left(\tau \right)$: Dedekind’s eta function (or Dedekind modular function), $J\left(\tau \right)$: Klein’s complete invariant, $\mathrm{i}$: imaginary unit, $\lambda \left(\tau \right)$: elliptic modular function and $y$: imaginary part of $z$

Referenced by:

Figure 20.3.2, Figure 20.3.2, §23.16

Permalink:

http://dlmf.nist.gov/23.16.F1

Encodings:

pdf, png

See also:

Annotations for §23.16 and Ch.23

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Symbols:

$\mathrm{i}$: imaginary unit, $\lambda \left(\tau \right)$: elliptic modular function, $x$: real part of $z$ and $y$: imaginary part of $z$

Referenced by:

§23.16

Permalink:

http://dlmf.nist.gov/23.16.F2

Encodings:

Vizualization, pdf, png

See also:

Annotations for §23.16 and Ch.23

ⓘ

Symbols:

$\eta \left(\tau \right)$: Dedekind’s eta function (or Dedekind modular function), $\mathrm{i}$: imaginary unit, $x$: real part of $z$ and $y$: imaginary part of $z$

Referenced by:

§23.16

Permalink:

http://dlmf.nist.gov/23.16.F3

Encodings:

Vizualization, pdf, png

See also:

Annotations for §23.16 and Ch.23

23.15 Definitions23.17 Elementary Properties

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