jacobiSD
Jacobi SD elliptic function
Syntax
Description
jacobiSD(
returns the Jacobi SD Elliptic Function of
u
,m
)u
and m
. If u
or
m
is an array, then jacobiSD
acts
element-wise.
Examples
Calculate Jacobi SD Elliptic Function for Numeric Inputs
jacobiSD(2,1)
ans = 3.6269
Call jacobiSD
on array inputs.
jacobiSD
acts element-wise when
u
or m
is an array.
jacobiSD([2 1 -3],[1 2 3])
ans = 3.6269 2.1629 -126.3078
Calculate Jacobi SD Elliptic Function for Symbolic Numbers
Convert numeric input to symbolic form using
sym
, and find the Jacobi SD elliptic function. For
symbolic input where u = 0
or m = 0
or
1
, jacobiSD
returns exact symbolic
output.
jacobiSD(sym(2),sym(1))
ans = sinh(2)
Show that for other values of u
or
m
, jacobiSD
returns an unevaluated
function call.
jacobiSD(sym(2),sym(3))
ans = jacobiSD(2, 3)
Find Jacobi SD Elliptic Function for Symbolic Variables or Expressions
For symbolic variables or expressions,
jacobiSD
returns the unevaluated function call.
syms x y f = jacobiSD(x,y)
f = jacobiSD(x, y)
Substitute values for the variables by using subs
,
and convert values to double by using double
.
f = subs(f, [x y], [3 5])
f = jacobiSD(3, 5)
fVal = double(f)
fVal = 0.0312
Calculate f
to higher precision using
vpa
.
fVal = vpa(f)
fVal = 0.031220579864538785956650143970485
Plot Jacobi SD Elliptic Function
Plot the Jacobi SD elliptic function using fcontour
. Set u
on the x-axis and m
on the y-axis by using the symbolic function f
with the variable order (u,m)
. Fill plot contours by setting Fill
to on
.
syms f(u,m) f(u,m) = jacobiSD(u,m); fcontour(f,'Fill','on') title('Jacobi SD Elliptic Function') xlabel('u') ylabel('m')
Input Arguments
u
— Input
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression
Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.
m
— Input
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression
Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.
More About
Jacobi SD Elliptic Function
The Jacobi SD elliptic function is
sd(u,m) = sn(u,m)/dn(u,m)
where sn and dn are the respective Jacobi elliptic functions.
The Jacobi elliptic functions are meromorphic and doubly periodic in their first
argument with periods 4K(m) and 4iK'(m), where K is the complete elliptic integral of the first kind, implemented
as ellipticK
.
Version History
Introduced in R2017b
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