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Plotting incomplete elliptic integral of 1st kind

complete elliptic integral of the first kindAsymptotic approximation to incomplete elliptic integral of third kind at a pole - determine constantApproximations of the incomplete elliptic integral of the second kindAsymptotic behavior of elliptic integral (first kind)Weierstrass $wp$ function inverts incomplete elliptic integralcomplete elliptic integral of the 1st kind with infinitely large argumentIncomplete elliptic integral of the second kind with negative parameterintegrating incomplete elliptic integral of first kindReal and imaginary parts for incomplete elliptic integral 1st kind with complex argumentIncomplete elliptic integral and Jacobi's form

0

$begingroup$

The incomplete elliptic integral of 1st kind is:
$$F(varphi,k)=int_0^varphi frac1sqrt1 - k^2 sin^2(x) mathrmdx$$
I wanted to set a small dataframe in order to plot myself some points of $F(varphi,k)$ for different $varphi$ and $k$. Here is the code I imagined:

v.phi <- seq(0, 2*pi, 1)
n.phi <- length(v.phi)
v.k <- seq(-1, +1, 0.5)
n.k <- length(v.k)
k <- rep(v.k, each = n.phi, times = 1)
phi <- rep(v.phi, each = 1, times = n.k)
df <- data.frame(k, phi)
func <- function(x, k) 1/sqrt(1 - (k*sin(x))^2)
df$area <- integrate(func,lower=0, upper=df$phi, k=df$k)

But this generates errors and I am obviously mistaking in constructing the new variable df$area... Could someone put me in the right way?

real-analysis elliptic-integrals

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asked Mar 12 at 10:28

AndrewAndrew

214

$endgroup$

add a comment | 

0

$begingroup$

The incomplete elliptic integral of 1st kind is:
$$F(varphi,k)=int_0^varphi frac1sqrt1 - k^2 sin^2(x) mathrmdx$$
I wanted to set a small dataframe in order to plot myself some points of $F(varphi,k)$ for different $varphi$ and $k$. Here is the code I imagined:

v.phi <- seq(0, 2*pi, 1)
n.phi <- length(v.phi)
v.k <- seq(-1, +1, 0.5)
n.k <- length(v.k)
k <- rep(v.k, each = n.phi, times = 1)
phi <- rep(v.phi, each = 1, times = n.k)
df <- data.frame(k, phi)
func <- function(x, k) 1/sqrt(1 - (k*sin(x))^2)
df$area <- integrate(func,lower=0, upper=df$phi, k=df$k)

But this generates errors and I am obviously mistaking in constructing the new variable df$area... Could someone put me in the right way?

real-analysis elliptic-integrals

share|cite|improve this question

asked Mar 12 at 10:28

AndrewAndrew

214

$endgroup$

add a comment | 

$begingroup$

The incomplete elliptic integral of 1st kind is:
$$F(varphi,k)=int_0^varphi frac1sqrt1 - k^2 sin^2(x) mathrmdx$$
I wanted to set a small dataframe in order to plot myself some points of $F(varphi,k)$ for different $varphi$ and $k$. Here is the code I imagined:

v.phi <- seq(0, 2*pi, 1)
n.phi <- length(v.phi)
v.k <- seq(-1, +1, 0.5)
n.k <- length(v.k)
k <- rep(v.k, each = n.phi, times = 1)
phi <- rep(v.phi, each = 1, times = n.k)
df <- data.frame(k, phi)
func <- function(x, k) 1/sqrt(1 - (k*sin(x))^2)
df$area <- integrate(func,lower=0, upper=df$phi, k=df$k)

But this generates errors and I am obviously mistaking in constructing the new variable df$area... Could someone put me in the right way?

real-analysis elliptic-integrals

share|cite|improve this question

asked Mar 12 at 10:28

AndrewAndrew

214

$endgroup$

v.phi <- seq(0, 2*pi, 1)
n.phi <- length(v.phi)
v.k <- seq(-1, +1, 0.5)
n.k <- length(v.k)
k <- rep(v.k, each = n.phi, times = 1)
phi <- rep(v.phi, each = 1, times = n.k)
df <- data.frame(k, phi)
func <- function(x, k) 1/sqrt(1 - (k*sin(x))^2)
df$area <- integrate(func,lower=0, upper=df$phi, k=df$k)

share|cite|improve this question

asked Mar 12 at 10:28

AndrewAndrew

214

share|cite|improve this question

asked Mar 12 at 10:28

AndrewAndrew

214

asked Mar 12 at 10:28

AndrewAndrew

214

asked Mar 12 at 10:28

AndrewAndrew

214