s17dl {NAGFWrappers} R Documentation

## s17dl: Hankel functions H_nu + a^(j)(z), j = 1 , 2, real a >= 0, complex z, nu=0 , 1 , 2 , . . .

### Description

s17dl returns a sequence of values for the Hankel functions H_ν + n^(1)(z) or H_ν + n^(2)(z) for complex z, non-negative ν and n = 0 , 1 , . . . , N - 1, with an option for exponential scaling.

### Usage

```s17dl(m, fnu, z, n, scal)
```

### Arguments

 `m` integer The kind of functions required. m = 1: The functions are H_ν^(1)(z). m = 2: The functions are H_ν^(2)(z). `fnu` double ν, the order of the first member of the sequence of functions. `z` complex The argument z of the functions. `n` integer N, the number of members required in the sequence H_ν^(m)(z) , H_ν + 1^(m)(z) , . . . , H_ν + N - 1^(m)(z). `scal` string The scaling option. scal='U': The results are returned unscaled. scal='S': The results are returned scaled by the factor e^ - iz when m = 1, or by the factor e^iz when m = 2.

### Details

R interface to the NAG Fortran routine S17DLF.

### Value

 `CY` complex array The N required function values: cy[i] contains H_ν + i - 1^(m)(z) for i=1 . . . N. `NZ` integer The number of components of cy that are set to zero due to underflow. If nz > 0, then if Im(z) > 0.0 and m = 1, or Im(z) < 0.0 and m = 2, elements cy , cy , . . . , cy[nz] are set to zero. In the complementary half-planes, nz simply states the number of underflows, and not which elements they are. `IFAIL` integer ifail =0 unless the function detects an error or a warning has been flagged (see the Errors section in Fortran library documentation).

NAG

### Examples

```
ifail<-0

m<-1

fnu<-0

z<-complex(1,0.3,0.4)

n<-2

scal<-'U'

s17dl(m,fnu,z,n,scal)

```

[Package NAGFWrappers version 24.0 Index]