theta

Theta series

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

theta(x)

Description

theta(x) represents the value of the theta series .

The theta series converges for all complex numbers x with positive real part.

Floating-point results are computed for floating-point arguments. For other arguments, the function returns symbolically with the imaginary part of complex numbers normalized to lie between zero and 2.

Environment Interactions

When called with a floating-point argument, the function is sensitive to the environment variable DIGITS which determines the numerical working precision.

Examples

Example 1

The theta series takes on large values for small positive arguments. Small values are taken on near I:

theta(0.001), theta(0.001 + I)

Example 2

Since the theta series is (2 i)-periodic, the imaginary part of complex arguments may be reduced:

theta(7 + 5*I)

For exact or symbolic arguments, a symbolic call is returned:

theta(3), theta(x)

Parameters

x

An arithmetical expression

Return Values

Arithmetical expression

See Also

MuPAD Functions

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