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Immediate Computable Access to Curated Contributed Data

Mock Theta Functions

Source Notebook

Definitions of the mock theta functions

Originator: Souichiro-Ikebe

(42 elements)

Examples

Basic Examples

Evaluate a function:

In[1]:=
ResourceData["Mock Theta Functions"][ "mt\[ScriptCapitalF]0"][.1 + .5 I]
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To identify functions and their orders:

In[2]:=
{<|"Order" -> 2, "Functions" -> {"mtA", "mtB", "mt\[Mu]"}, "Notation" -> {A[q], B[q], \[Mu][q]}|>, <|"Order" -> 3, "Functions" -> {"mt\[Chi]", "mtf", "mt\[Omega]", "mt\[Phi]", "mt\[Psi]", "mt\[Rho]"}, "Notation" -> {\[Chi][q], f[q], \[Omega][q], \[Phi][q], \[Psi][q], \[Rho][ q]}|>, <|"Order" -> 5, "Functions" -> {"mt\[Chi]0", "mt\[Chi]1", "mtf0", "mtf1", "mtF0", "mtF15", "mt\[Phi]0", "mt\[Phi]1", "mt\[Psi]0", "mt\[Psi]1"}, "Notation" -> {Subscript[\[Chi], 0][q], Subscript[\[Chi], 1][q], Subscript[f, 0][q], Subscript[f, 1][q], Subscript[F, 0][q], Subscript[F, 1][q], Subscript[\[Phi], 0][q], Subscript[\[Phi], 1][q], Subscript[\[Psi], 0][q], Subscript[\[Psi], 1][q]}|>, <|"Order" -> 6, "Functions" -> {"mt\[Gamma]", "mt\[Lambda]", "mt\[Mu]6", "mt\[Phi]6", "mt\[Psi]6", "mt\[Rho]6", "mt\[Sigma]"}, "Notation" -> {\[Gamma][q], \[Lambda][q], \[Mu][q], \[Phi][ q], \[Psi][q], \[Rho][q], \[Sigma][q]}|>, <|"Order" -> 7, "Functions" -> {"mt\[ScriptCapitalF]0", "mt\[ScriptCapitalF]1", "mt\[ScriptCapitalF]2"}, "Notation" -> {Subscript[\[ScriptCapitalF], 0][q], Subscript[\[ScriptCapitalF], 1][q], Subscript[\[ScriptCapitalF], 2][q]}|>, <|"Order" -> 8, "Functions" -> {"mtS0", "mtS1", "mtT0", "mtT1", "mtU0", "mtU1", "mtV0", "mtV1"}, "Notation" -> {Subscript[S, 0][q], Subscript[S, 1][q], Subscript[T, 0][q], Subscript[T, 1][q], Subscript[U, 0][q], Subscript[U, 1][q], Subscript[V, 0][q], Subscript[V, 1][q]}|>, <|"Order" -> 10, "Functions" -> {"mt\[CapitalPhi]", "mt\[CapitalPsi]", "mtX", "mt\[CapitalChi]"}, "Notation" -> {\[CapitalPhi][q], \[CapitalPsi][q], X[q], \[CapitalChi][q]}|>} // Dataset
Out[2]=

Visualize the functions:

In[3]:=
Module[{\[Delta] = 0.005`}, ListContourPlot[ Table[If[Abs[x + I y] >= 0.999`, None, Im[ResourceData["Mock Theta Functions"]["mtB"][ x + I y]]], {y, -0.999`, 0.999`, \[Delta]}, {x, -0.999`, 0.999`, \[Delta]}], ClippingStyle -> Automatic, Frame -> False, MeshFunctions -> {#3 &}, ColorFunction -> (ColorData["Rainbow"][#1] &), Axes -> False, Background -> Black]]
Out[3]=
In[4]:=
Module[{\[Delta] = 0.005`}, ListPlot3D[ Table[If[Abs[x + I y] >= 0.999`, None, Im[ResourceData["Mock Theta Functions"]["mtB"][ x + I y]]], {y, -0.999`, 0.999`, \[Delta]}, {x, -0.999`, 0.999`, \[Delta]}], ClippingStyle -> Automatic, Boxed -> False, MeshFunctions -> {#3 &}, ColorFunction -> (ColorData["Rainbow"][#1] &), Axes -> False, Background -> Black]]
Out[4]=

Enrique Zeleny, "Mock Theta Functions" from the Wolfram Data Repository (2022)  

Data Resource History

  • Date Created:

Source Metadata

  • Language: Japanese
  • Source: http://math-functions-1.watson.jp/sub2_qspec_090.html
  • Citation: Graphics Library of Special Functions

Data Downloads

Publisher Information

  • Prepared for the Wolfram Data Repository By: Enrique Zeleny
  • Publisher of Record: Enrique Zeleny