[sf.cmath.cyl.bessel.i]

# 29 Numerics library [[numerics]](./#numerics)

## 29.7 Mathematical functions for floating-point types [[c.math]](c.math#sf.cmath.cyl.bessel.i)

### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#cyl.bessel.i)

#### 29.7.6.8 Regular modified cylindrical Bessel functions [sf.cmath.cyl.bessel.i]

[ð](#lib:cyl_bessel_i)

`floating-point-type cyl_bessel_i(floating-point-type nu, floating-point-type x);
float        cyl_bessel_if(float nu, float x);
long double  cyl_bessel_il(long double nu, long double x);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10224)

*Effects*: These functions compute
the regular modified cylindrical Bessel functions
of their respective argumentsnu and x[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10231)

*Returns*: IÎ½(x),
where IÎ½ is given by Formula [29.28](#eq:sf.cmath.cyl.bessel.i),Î½ is nu, andx is x[.](#2.sentence-1)

IÎ½(x)=iâÎ½JÎ½(ix)=ââk=0(x/2)Î½+2kk!Î(Î½+k+1)Â , forÂ xâ¥0(29.28)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10244)

*Remarks*: The effect of calling each of these functions
is implementation-defined
if nu >= 128[.](#3.sentence-1)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10250)

See also [[sf.cmath.cyl.bessel.j]](sf.cmath.cyl.bessel.j "29.7.6.9 Cylindrical Bessel functions of the first kind")[.](#4.sentence-1)
