Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 MathieuEllipticCos

Source Notebook

Evaluate the cosine-elliptic Mathieu function

Contributed by: S. M. Blinder

ResourceFunction["MathieuEllipticCos"][n, x, q]

gives the nth even Mathieu function cen(x,q).

Details

Mathematical function, suitable for both symbolic and numerical manipulation.
The Mathieu function cen(x,q) satisfies the equation y′′+(an(q)-2qcos(2x))y=0 where, for nonnegative integers n, an(q) is the nth characteristic value for even Mathieu functions.
The function cen(x,q) is π-periodic for even n, and 2π-periodic for odd n.
For certain special arguments, ResourceFunction["MathieuEllipticCos"] automatically evaluates to exact values.
ResourceFunction["MathieuEllipticCos"] can be evaluated to arbitrary numerical precision.
ResourceFunction["MathieuEllipticCos"] automatically threads over lists.

Examples

Basic Examples (2) 

Evaluate the ce1(x,0) function:

In[1]:=
ResourceFunction["MathieuEllipticCos"][1, x, 0]
Out[1]=

Evaluate ce2(2,2) numerically:

In[2]:=
N[ResourceFunction["MathieuEllipticCos"][2, 2, 2]]
Out[2]=

Applications (1) 

Function plots for q=2:

In[3]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/e66dc87b-2390-44ed-ad59-0a9c145e8820"]
Out[3]=

Neat Examples (1) 

Visualize an eigenfunction of the Laplace equation in an ellipse that vanishes at the boundary:

In[4]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/fc64d6fe-4f6e-4aed-b1cf-c0f51a47f4f6"]
Out[4]=

Version History

  • 1.0.0 – 28 March 2022

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