Jacobi theta functions at x=0 for 0 \le q <1

Jacobi theta functions at \(x=0\) for \(0 \le q <1\)#

Jacobi theta function \(\theta'_1(q)\)#

math53.jacobi_theta1p(q)#

Returns the Jacobi theta function \(\theta'_1(q) = \partial\theta_1(x,q)/\partial x\) at \(x=0\) for \(0 \le q <1\). See also Wikipedia [1424], MathWorld [1039], MathWorld [286], NIST [503], Ehrhardt [309] (3.2.14.1).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.JacobiTheta1p(0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.JacobiTheta1p('0.51')
ereal('5.3518479027559984754E-1')

Jacobi theta function \(\theta_2(q)\)#

math53.jacobi_theta02(q)#

Returns the Jacobi theta function \(\theta_2(q) = \theta_2(0,q)\) for \(0 \le q <1\). See also Wikipedia [1424], MathWorld [1039], NIST [503], Ehrhardt [309] (3.2.14.2).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.JacobiTheta2(0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.JacobiTheta2('0.51')
ereal('5.3518479027559984754E-1')

Jacobi theta function \(\theta_3(q)\)#

math53.jacobi_theta03(q)#

Returns the Jacobi theta function \(\theta_3(q) = \theta_3(0,q)\) for \(0 \le q <1\). See also Wikipedia [1424], MathWorld [1039], NIST [503], Ehrhardt [309] (3.2.14.3).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.JacobiTheta3(0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.JacobiTheta3('0.51')
ereal('5.3518479027559984754E-1')

Jacobi theta function \(\theta_4(q)\)#

math53.jacobi_theta04(q)#

Returns the Jacobi theta function \(\theta_4(q) = \theta_4(0,q)\) for \(-1 < q <1\). See also Wikipedia [1424], MathWorld [1039], NIST [503], Ehrhardt [309] (3.2.14.4).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.JacobiTheta4(0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.JacobiTheta4('0.51')
ereal('5.3518479027559984754E-1')
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