EllipticThetaPrime

The u-derivative of the Jacobi theta function, $\vartheta_a'(u,q) = \dfrac{\partial}{\partial u}\vartheta_a(u,q)$, $a=1,2,3,4$, Wolfram's nome convention $|q|<1$.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageEllipticThetaPrime!↗

EllipticThetaPrime(a, u, q)the u-derivative of the a-th Jacobi theta function (a = 1, 2, 3, or 4), argument u, nome q.

Typed signatures

Type	Package	Applies
(number, number, number) -> number	analytic	always

Domain: Special functions

Details

• Shares EllipticTheta's nome convention, series-convergence rule, and decline conditions — see there.
• The termwise u-derivative of DLMF 20.2.1-20.2.4, verified against mpmath's jtheta(a, u, q, derivative=1) and a Wolfram kernel at complex u, complex q, and real negative q.
• Numeric only — a symbolic u or q stays unevaluated; a floating-point argument (or N()) evaluates directly.

Examples

25 more kept as data, checked against the oracles

Basic #

A floating-point argument evaluates directly to a decimal

live ↗

In$N(\mathrm{EllipticThetaPrime}(3, 0.3, 0.2))$Out$-0.463\,650\,062\,407\,080\,4$

Known value · mpmath 1.3.0 jtheta(derivative=1)

Scope #

The a = 1 theta function's derivative

live ↗

In$N(\mathrm{EllipticThetaPrime}(1, 0.3, 0.2))$Out$1.178\,007\,371\,087\,324$

Known value · mpmath 1.3.0 jtheta(derivative=1)

A complex argument u

live ↗

In$N(\mathrm{EllipticThetaPrime}(3, 0.3+0.1i, 0.2))$Out$-0.473\,682\,807\,676\,938\,2-0.134\,840\,072\,893\,700\,92i$

Known value · mpmath 1.3.0 jtheta(derivative=1)

Possible issues #

|q| ≥ 1 is declined — the series diverges there

live ↗

In$N(\mathrm{EllipticThetaPrime}(3, 0.3, 1))$Out$\mathrm{EllipticThetaPrime}(3, 0.3, 1)$

Symbolic arguments are left unevaluated rather than guessed at

live ↗

In$\mathrm{EllipticThetaPrime}(3, u, q)$Out$\mathrm{EllipticThetaPrime}(3, u, q)$

Same gap as EllipticTheta (the true value is tracked there, not repeated per head).

live ↗

In$N(\mathrm{EllipticThetaPrime}(1, 10^{30}, \frac{1}{π}))$Out$\mathrm{EllipticThetaPrime}(1, 1.0\cdot10^{30}, 0.318\,309\,886\,183\,790\,671\,538)$

About

Examples	31
Checked against	Wolfram Language 30 agree1 differ
Crosswalk	Wolfram Language

See also: EllipticTheta