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23 Weierstrass Elliptic and Modular Functions Modular Functions 23.15 Definitions 23.17 Elementary Properties

§23.16 Graphics

Notes:: These graphics were produced at NIST.
Keywords:: modular functions
Permalink:: http://dlmf.nist.gov/23.16

See Figures 23.16.1–23.16.3 for the modular functions $\mathop{\lambda\/}\nolimits$ , $\mathop{J\/}\nolimits$ , and $\mathop{\eta\/}\nolimits$ . 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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Figure 23.16.1: Modular functions $\mathop{\lambda\/}\nolimits\!\left(iy\right)$ , $\mathop{J\/}\nolimits\!\left(iy\right)$ , $\mathop{\eta\/}\nolimits\!\left(iy\right)$ for $0\leq y\leq 3$ . See also Figure 20.3.2.

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Symbols:: $\mathop{\eta\/}\nolimits\!\left(\tau\right)$ : Dedekind’s eta function (or Dedekind modular function), $\mathop{J\/}\nolimits\!\left(\tau\right)$ : Klein’s complete invariant, $\mathop{\lambda\/}\nolimits\!\left(\tau\right)$ : elliptic modular function and : imaginary part of
Referenced by:: Figure 20.3.2, Figure 20.3.2, §23.16
Permalink:: http://dlmf.nist.gov/23.16.F1
Encodings:: pdf, png

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Figure 23.16.2: Elliptic modular function $\mathop{\lambda\/}\nolimits\!\left(x+iy\right)$ for $-0.25\leq x\leq 0.25$ , $0.005\leq y\leq 0.1$ .

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Symbols:: $\mathop{\lambda\/}\nolimits\!\left(\tau\right)$ : elliptic modular function, : real part of and : imaginary part of
Referenced by:: §23.16
Permalink:: http://dlmf.nist.gov/23.16.F2
Encodings:: VRML, X3D, pdf, png

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Figure 23.16.3: Dedekind’s eta function $\mathop{\eta\/}\nolimits\!\left(x+iy\right)$ for $-0.0625\leq x\leq 0.0625$ , $0.0001\leq y\leq 0.07$ .

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Symbols:: $\mathop{\eta\/}\nolimits\!\left(\tau\right)$ : Dedekind’s eta function (or Dedekind modular function), : real part of and : imaginary part of
Referenced by:: §23.16
Permalink:: http://dlmf.nist.gov/23.16.F3
Encodings:: VRML, X3D, pdf, png

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 23.15 Definitions 23.17 Elementary Properties

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