Function Repository Resource:

# MockTheta

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:

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Evaluate a mock theta function for numeric input:

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### Scope (1)

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

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### Properties and Relations (1)

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

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### Possible Issues (2)

Some results may contain small imaginary components:

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Chop will remove the small component:

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## Version History

• 1.0.0 – 16 December 2019