Hello there,
I was fooling around with an old formula i came up with for calculating the inductance of a coil and was comparing the results to several other formulas, including one i found on Wikipedia. The formulas involve complete elliptic integrals of the first and second kind. I then went back on the web and looked for the formula for the integral that usually just goes by the name "E" and comes in two forms, E(a,x) and just E(x). The form which i need is E(x) but it comes from E(pi/2,x) so those two are equivalent.
The real problem came in when i went to calculate a formula using E(x). I found two different results, both in fairly respectable places. The two different results are:
E(0.4)=1.399 {Wolfram using EllipticE(0.4), using k}
and
E(0.4)=1.505 {Direct calculation, Using k^2}
Those are not exact but should be within plus or minus 0.001.
I looked into this and found that the formula for this integral was:
integrate(y(x),x,0,pi/2)
where ONE FORM OF y(x) is:
y(x)=1/(1-k^2*sin(x)^2)
and that formula results in E(0.4)=1.505
Now interestingly, the OTHER FORM OF y(x) is:
y(x)=1/(1-k*sin(x)^2)
and this form results in E(0.4)=1.399.
What do you think?
I was fooling around with an old formula i came up with for calculating the inductance of a coil and was comparing the results to several other formulas, including one i found on Wikipedia. The formulas involve complete elliptic integrals of the first and second kind. I then went back on the web and looked for the formula for the integral that usually just goes by the name "E" and comes in two forms, E(a,x) and just E(x). The form which i need is E(x) but it comes from E(pi/2,x) so those two are equivalent.
The real problem came in when i went to calculate a formula using E(x). I found two different results, both in fairly respectable places. The two different results are:
E(0.4)=1.399 {Wolfram using EllipticE(0.4), using k}
and
E(0.4)=1.505 {Direct calculation, Using k^2}
Those are not exact but should be within plus or minus 0.001.
I looked into this and found that the formula for this integral was:
integrate(y(x),x,0,pi/2)
where ONE FORM OF y(x) is:
y(x)=1/(1-k^2*sin(x)^2)
and that formula results in E(0.4)=1.505
Now interestingly, the OTHER FORM OF y(x) is:
y(x)=1/(1-k*sin(x)^2)
and this form results in E(0.4)=1.399.
What do you think?