Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 MockTheta

Source Notebook

Implement the Ramanujan mock theta functions

Contributed by: Paco Jain (Wolfram Research)

ResourceFunction["MockTheta"]["type", q]

gives the value of the mock theta function of type "type" at q.

ResourceFunction["MockTheta"]["Types"]

gives a list of available types.

Details and Options

Mathematical function, suitable for both symbolic and numerical manipulation.
The mock theta functions are defined only in the region Abs[q]<1.
Available values for "type" are: "2A", "2B", "2Mu", "3Chi", "3F", "3Nu", "3Omega", "3Phi", "3Psi", "3Rho", "3Sigma", "3Xi", "5CapitalF0", "5CapitalF1", "5Chi0", "5Chi1", "5F0", "5F1", "5Phi0", "5Phi1", "5Psi0", "5Psi1", "6Beta", "6Gamma", "6Lambda", "6Mu", "6Nu", "6Phi", "6Psi", "6Rho", "6Sigma", "6Xi", "7F0", "7F1", "7F2", "8S0", "8S1", "8T0", "8T1", "8U0", "8U1", "8V0", "8V1", "10CapitalChi", "10Chi", "10Phi" and "10Psi".

Examples

Basic Examples (2) 

Evaluate a mock theta function for symbolic input:

In[1]:=
ResourceFunction["MockTheta"]["6Sigma", q]
Out[1]=

Evaluate a mock theta function for numeric input:

In[2]:=
ResourceFunction["MockTheta"]["3Psi", 0.68]
Out[2]=

Scope (1) 

Obtain a list of the allowed types of mock theta functions:

In[3]:=
ResourceFunction["MockTheta"]["Types"]
Out[3]=

Properties and Relations (1) 

For generic exact values or symbolic input, mock theta functions are evaluated in terms of QHypergeometricPFQ:

In[4]:=
ResourceFunction["MockTheta"]["2A", 1/2]
Out[4]=

Possible Issues (2) 

Some results may contain small imaginary components:

In[5]:=
ResourceFunction["MockTheta"]["6Sigma", -.4]
Out[5]=

Chop will remove the small component:

In[6]:=
Chop@ResourceFunction["MockTheta"]["6Sigma", -.4]
Out[6]=

Version History

  • 1.0.0 – 16 December 2019

Related Resources

License Information