Bessel_i_nu_scaled
Bessel-i-nu-scaled-func
Definition:
/math-2e520ed3e3b41bf485e6966a19bc075c.png "i\_nu\_scaled = bessel\_i\_nu\_scaled(x,nu)")
evaluates an approximation to the modified Bessel function of the first kind /math-d47ff7d464b7eda422ec4833219fad68.png "e^{-x}I_{\frac \nu 4}(x)")
, where the order =-3, -2, -1, 1, 2 or 3 and x is real and positive. For positive orders it may also be called with x=0, since /math-fd10bcd475f2f3d023b9d9b0c7e2301f.png "I_{\frac \nu 4}(0)=0")
when /math-4fdefba26320686bb2bd0579a0df421c.png "\nu")
> 0. For negative orders the formula
/math-31158ca4ac5f5425554299c0c07b5e80.png "I_{\frac{-\nu }4}(x)=I_{\frac \upsilon 4}(x)+\frac 2\pi \sin (\frac{\pi \upsilon }4)K_{\frac \upsilon 4}(x)")
is used prior to multiplication by the scale factor /math-3539476280ded0b8ae128f624f212b68.png "e^{-x}")
.
For more information please review the s18ecc function in the NAG document.
Parameters:
- x (input, double)
- The argument x of the function.
- Constraints:
x>0.0 when nu<0,
x???0.0 when nu>0.
/math-0288bde0c2d593f2b5766f61b826a650.png "nu")
(input, int)- The argument of the function.
- Constraints:
/math-444b9207f37c2461a13f9bd94a0ba099.png "1\leq abs(nu)\leq 3")
/math-a58edbbeb0740345525c996ffc37c64c.png "i\_nu\_scaled")
(output, double)- Approximation of the modified Bessel function of the first kind.