RamanujanTauTheta
gives the Ramanujan tau theta function .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- Apart from a sign,
gives the phase of the Ramanujan L-function
.
- For certain special arguments, RamanujanTauTheta automatically evaluates to exact values.
- RamanujanTauTheta can be evaluated to arbitrary numerical precision.
- RamanujanTauTheta automatically threads over lists.
Examples
open allclose allBasic Examples (3)
Scope (19)
Numerical Evaluation (5)
Specific Values (2)
Visualization (2)
Plot the RamanujanTauTheta:
Plot the real part of RamanujanTauTheta function:
Plot the imaginary part of RamanujanTauTheta function:
Function Properties (10)
RamanujanTauTheta is defined for all real values:
Function range of RamanujanTauTheta:
RamanujanTauTheta threads over lists:
RamanujanTauTheta is an analytic function of x:
RamanujanTauTheta is neither non-increasing nor non-decreasing:
RamanujanTauTheta is not injective:
RamanujanTauTheta is surjective:
RamanujanTauTheta is neither non-negative nor non-positive:
RamanujanTauTheta has no singularities or discontinuities:
RamanujanTauTheta is neither convex nor concave:
Applications (3)
Contour plot of the absolute value of RamanujanTauTheta:
The first 10 Gram points of RamanujanTauL:
Plot of RamanujanTauZ and Gram points:
Properties & Relations (1)
On the critical line, RamanujanTauTheta gives the phase of RamanujanTauL up to a sign:
RamanujanTauL can be expressed in terms of RamanujanTauTheta:
Text
Wolfram Research (2007), RamanujanTauTheta, Wolfram Language function, https://reference.wolfram.com/language/ref/RamanujanTauTheta.html.
CMS
Wolfram Language. 2007. "RamanujanTauTheta." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RamanujanTauTheta.html.
APA
Wolfram Language. (2007). RamanujanTauTheta. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RamanujanTauTheta.html