I have forgotten
my Password

Or login with:

  • Facebookhttp://facebook.com/
  • Googlehttps://www.google.com/accounts/o8/id
  • Yahoohttps://me.yahoo.com
get GPL
COST (GBP)
this unit 5.62
sub units 0.50
+
0
MathsSpecialBesselI

I1

Modified Bessel function of the first kind, with order one and exponential scaling.
Controller: CodeCogs

get GPL add to cart

Dependents

Info

Interface

C++
Excel

Overview

Return a solution to the Modified Bessel Function of the first kind with order one.

The differential equation is called the modified Bessel's equation of order one, with the solution known as the modified Bessel function, with two fundamental solutions: I_1(z) and I_{-1}(z), where

where \Gamma(n) is the gamma function.

I1 Exp

 
doubleI1_expdoublex )
Returns exponentially scaled modified Bessel function of the first kind, with order one.

The function is defined as I_1(x) \exp(x) = -i \exp(-|x|) J_1(i x).

See aslo Maths/Special/Bessel/I/I

Accuracy:

<pre> Relative error: arithmetic domain # trials peak rms IEEE 0,30 30000 2.0e-15 2.0e-16 </pre>

References:

Cephes Math Library Release 2.8: June, 2000

Example 1

#include <codecogs/maths/special/bessel/i/i1.h>
#include <stdio.h>
 
int main()
{
  using namespace Maths::Special::Bessel::I;
  for(double x=0; x<6; x+=1)
  {
    double y=I1_exp(x);
    printf("\n I1_exp(%.1lf)=%lf", x,y);
  }
  return 0;
}
Output:
I1_exp(0.0)=0.000000
I1_exp(1.0)=0.207910
I1_exp(2.0)=0.215269
I1_exp(3.0)=0.196827
I1_exp(4.0)=0.178751
I1_exp(5.0)=0.163972

Parameters

xinput argument

Authors

Stephen L. Moshier. Copyright 1984, 1987, 2000
Documentation by Will Bateman (August 2005)
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.


I1

 
doubleI1doublex )[inline]
Returns modified Bessel function of the first kind, with order one (v=1).

The function is defined as I_1(x) = -i J_1(i x)

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

Accuracy:

<pre> Relative error: arithmetic domain # trials peak rms DEC 0, 30 3400 1.2e-16 2.3e-17 IEEE 0, 30 30000 1.9e-15 2.1e-16</pre>

References:

Cephes Math Library Release 2.8: June, 2000

Example 2

#include <codecogs/maths/special/bessel/i/i1.h>
#include <stdio.h>
 
int main()
{
  for(double x=0; x<6; x+=1)
  {
    double y=Maths::Special::Bessel::I::I1(x);
    printf("\n I1(%.1lf)=%lf", x,y);
  }
  return 0;
}
Output:
I1(0.0)=0.000000
I1(1.0)=0.565159
I1(2.0)=1.590637
I1(3.0)=3.953370
I1(4.0)=9.759465
I1(5.0)=24.335642

Parameters

xValue to be transformed.

Authors

Stephen L. Moshier. Copyright 1984, 1987, 2000
Documentation by Will Bateman (August 2005)
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.