NevilleThetaS
✖
NevilleThetaS
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- NevilleThetaS[z,m] is a meromorphic function of and has a complicated branch cut structure in the complex plane.
- For certain special arguments, NevilleThetaS automatically evaluates to exact values.
- NevilleThetaS can be evaluated to arbitrary numerical precision.
- NevilleThetaS automatically threads over lists.
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Scope (27)Survey of the scope of standard use cases
Numerical Evaluation (6)
https://wolfram.com/xid/0e5cvs7fqvuevm-l274ju
https://wolfram.com/xid/0e5cvs7fqvuevm-wlv0g
https://wolfram.com/xid/0e5cvs7fqvuevm-b0wt9
https://wolfram.com/xid/0e5cvs7fqvuevm-hwtopb
The precision of the output tracks the precision of the input:
https://wolfram.com/xid/0e5cvs7fqvuevm-y7k4a
https://wolfram.com/xid/0e5cvs7fqvuevm-hfml09
Evaluate efficiently at high precision:
https://wolfram.com/xid/0e5cvs7fqvuevm-di5gcr
https://wolfram.com/xid/0e5cvs7fqvuevm-bq2c6r
Compute average-case statistical intervals using Around:
https://wolfram.com/xid/0e5cvs7fqvuevm-cw18bq
Compute the elementwise values of an array:
https://wolfram.com/xid/0e5cvs7fqvuevm-thgd2
Or compute the matrix NevilleThetaS function using MatrixFunction:
https://wolfram.com/xid/0e5cvs7fqvuevm-o5jpo
Specific Values (3)
Values at corners of the fundamental cell:
https://wolfram.com/xid/0e5cvs7fqvuevm-srsfi
NevilleThetaS for special values of elliptic parameter:
https://wolfram.com/xid/0e5cvs7fqvuevm-gco8d
https://wolfram.com/xid/0e5cvs7fqvuevm-c4t14z
Find the first positive maximum of NevilleThetaS[x,1/2]:
https://wolfram.com/xid/0e5cvs7fqvuevm-f2hrld
https://wolfram.com/xid/0e5cvs7fqvuevm-fr3tb7
Visualization (3)
Plot the NevilleThetaS functions for various values of the parameter:
https://wolfram.com/xid/0e5cvs7fqvuevm-ecj8m7
Plot NevilleThetaS as a function of its parameter :
https://wolfram.com/xid/0e5cvs7fqvuevm-du62z6
https://wolfram.com/xid/0e5cvs7fqvuevm-ouu484
https://wolfram.com/xid/0e5cvs7fqvuevm-bzsmnc
Function Properties (11)
The real domain of NevilleThetaS:
https://wolfram.com/xid/0e5cvs7fqvuevm-cl7ele
The complex domain of NevilleThetaS:
https://wolfram.com/xid/0e5cvs7fqvuevm-de3irc
https://wolfram.com/xid/0e5cvs7fqvuevm-evf2yr
https://wolfram.com/xid/0e5cvs7fqvuevm-fphbrc
NevilleThetaS threads elementwise over lists:
https://wolfram.com/xid/0e5cvs7fqvuevm-71t8n
is an analytic function of for :
https://wolfram.com/xid/0e5cvs7fqvuevm-gva6yl
is neither non-decreasing nor non-increasing:
https://wolfram.com/xid/0e5cvs7fqvuevm-2ra8g
https://wolfram.com/xid/0e5cvs7fqvuevm-c9npzh
https://wolfram.com/xid/0e5cvs7fqvuevm-b5buvp
https://wolfram.com/xid/0e5cvs7fqvuevm-patce
https://wolfram.com/xid/0e5cvs7fqvuevm-bcrbvs
is neither non-negative nor non-positive for noninteger :
https://wolfram.com/xid/0e5cvs7fqvuevm-dvzykj
has no singularities or discontinuities for noninteger :
https://wolfram.com/xid/0e5cvs7fqvuevm-fyfbxx
https://wolfram.com/xid/0e5cvs7fqvuevm-5vh4e
is affine only for and otherwise it is neither convex nor concave:
https://wolfram.com/xid/0e5cvs7fqvuevm-l0srvu
TraditionalForm formatting:
https://wolfram.com/xid/0e5cvs7fqvuevm-mw90mm
Differentiation (2)
Series Expansions (2)
Find the Taylor expansion using Series:
https://wolfram.com/xid/0e5cvs7fqvuevm-ewr1h8
Plots of the first three approximations around :
https://wolfram.com/xid/0e5cvs7fqvuevm-binhar
The Taylor expansion for small elliptic parameter :
https://wolfram.com/xid/0e5cvs7fqvuevm-jwxla7
https://wolfram.com/xid/0e5cvs7fqvuevm-ot937
Generalizations & Extensions (1)Generalized and extended use cases
NevilleThetaS can be applied to power series:
https://wolfram.com/xid/0e5cvs7fqvuevm-dyr330
Applications (7)Sample problems that can be solved with this function
Plot over the arguments' plane:
https://wolfram.com/xid/0e5cvs7fqvuevm-1ida1
Conformal map from a unit triangle to the unit disk:
https://wolfram.com/xid/0e5cvs7fqvuevm-b4mjvn
Show points before and after the map:
https://wolfram.com/xid/0e5cvs7fqvuevm-d5shw5
https://wolfram.com/xid/0e5cvs7fqvuevm-bh08vt
Uniformization of a Fermat cubic :
https://wolfram.com/xid/0e5cvs7fqvuevm-ku82s
https://wolfram.com/xid/0e5cvs7fqvuevm-iwlvkn
Verify that points on the curve satisfy :
https://wolfram.com/xid/0e5cvs7fqvuevm-f37x35
Current flow in a rectangular conducting sheet with voltage applied at a pair of opposite corners:
https://wolfram.com/xid/0e5cvs7fqvuevm-gmmm
https://wolfram.com/xid/0e5cvs7fqvuevm-op1mqd
Parametrize a lemniscate by arc length:
https://wolfram.com/xid/0e5cvs7fqvuevm-b9pj2c
Show the classical and arc length parametrizations:
https://wolfram.com/xid/0e5cvs7fqvuevm-f0sed9
https://wolfram.com/xid/0e5cvs7fqvuevm-bgqae0
Complex parametrization of a sphere:
https://wolfram.com/xid/0e5cvs7fqvuevm-vre9j
The square of all points on the complex sphere is 1:
https://wolfram.com/xid/0e5cvs7fqvuevm-dszg0y
https://wolfram.com/xid/0e5cvs7fqvuevm-gprxeo
Conformal map from an ellipse to the unit disk:
https://wolfram.com/xid/0e5cvs7fqvuevm-f3w5wn
https://wolfram.com/xid/0e5cvs7fqvuevm-exvlr9
Properties & Relations (4)Properties of the function, and connections to other functions
Basic simplifications are automatically carried out:
https://wolfram.com/xid/0e5cvs7fqvuevm-ojczlk
https://wolfram.com/xid/0e5cvs7fqvuevm-by5pcs
All Neville theta functions are a multiple of shifted NevilleThetaS:
https://wolfram.com/xid/0e5cvs7fqvuevm-b1re76
https://wolfram.com/xid/0e5cvs7fqvuevm-dnppg4
https://wolfram.com/xid/0e5cvs7fqvuevm-l5x9z
Use FullSimplify for expressions containing Neville theta functions:
https://wolfram.com/xid/0e5cvs7fqvuevm-65dsy
Numerically find a root of a transcendental equation:
https://wolfram.com/xid/0e5cvs7fqvuevm-gst1er
Wolfram Research (1996), NevilleThetaS, Wolfram Language function, https://reference.wolfram.com/language/ref/NevilleThetaS.html.
Text
Wolfram Research (1996), NevilleThetaS, Wolfram Language function, https://reference.wolfram.com/language/ref/NevilleThetaS.html.
Wolfram Research (1996), NevilleThetaS, Wolfram Language function, https://reference.wolfram.com/language/ref/NevilleThetaS.html.
CMS
Wolfram Language. 1996. "NevilleThetaS." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NevilleThetaS.html.
Wolfram Language. 1996. "NevilleThetaS." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NevilleThetaS.html.
APA
Wolfram Language. (1996). NevilleThetaS. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NevilleThetaS.html
Wolfram Language. (1996). NevilleThetaS. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NevilleThetaS.html
BibTeX
@misc{reference.wolfram_2024_nevillethetas, author="Wolfram Research", title="{NevilleThetaS}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/NevilleThetaS.html}", note=[Accessed: 10-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_nevillethetas, organization={Wolfram Research}, title={NevilleThetaS}, year={1996}, url={https://reference.wolfram.com/language/ref/NevilleThetaS.html}, note=[Accessed: 10-January-2025
]}