Neville theta functions

Neville theta functions#

Neville \(\theta_s(x,k)\)#

math53.neville_theta_s(x, k)#

Returns the Neville theta function \(\displaystyle \theta_s(x,k) = \frac{2K(k)}{\pi} \frac{\theta_1(v,q(k))}{\theta'_1(0,q(k))}, \quad v = \frac{\pi x}{2K(k)}, |k| \le 1\), and \(q(k)\) is the elliptic nome.

See also: Wikipedia [1437], MathWorld [290], Ehrhardt [309] (3.2.15.1).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.NevilleThetaS(1.5, 0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.NevilleThetaS(1.5, '0.51')
ereal('5.3518479027559984754E-1')

Neville \(\theta_c(x,k)\)#

math53.neville_theta_c(x, k)#

Returns the Neville theta function \(\displaystyle \theta_c(x,k) = \frac{\theta_2(v,q(k))}{\theta_2(0,q(k))}, \quad v = \frac{\pi x}{2K(k)}, |k| \le 1\), and \(q(k)\) is the elliptic nome.

See also: Wikipedia [1437], MathWorld [287], Ehrhardt [309] (3.2.15.2).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.NevilleThetaC(1.5, 0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.NevilleThetaC(1.5, '0.51')
ereal('5.3518479027559984754E-1')

Neville \(\theta_d(x,k)\)#

math53.neville_theta_d(x, k)#

Returns the Neville theta function \(\displaystyle \theta_d(x,k) = \frac{\theta_3(v,q(k))}{\theta_3(0,q(k))}, \quad v = \frac{\pi x}{2K(k)}, |k| \le 1\), and \(q(k)\) is the elliptic nome.

See also: Wikipedia [1437], MathWorld [288], Ehrhardt [309] (3.2.15.3).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.NevilleThetaD(1.5, 0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.NevilleThetaD(1.5, '0.51')
ereal('5.3518479027559984754E-1')

Neville \(\theta_n(x,k)\)#

math53.neville_theta_n(x, k)#

Returns the Neville theta function \(\displaystyle \theta_n(x,k) = \frac{\theta_4(v,q(k))}{\theta_4(0,q(k))}, \quad v = \frac{\pi x}{2K(k)}, |k| \le 1\), and \(q(k)\) is the elliptic nome.

See also: Wikipedia [1437], MathWorld [289], Ehrhardt [309] (3.2.15.4).

An example in Python

>>> from xlcalcnet import ereal
>>> ereal.NevilleThetaN(1.5, 0.5)
ereal('5.2359877559829887307E-1')
>>> ereal.NevilleThetaN(1.5, '0.51')
ereal('5.3518479027559984754E-1')
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