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### 9.45 `BESSEL_YN`

— Bessel function of the second kind

*Description*:`BESSEL_YN(N, X)`

computes the Bessel function of the second kind of order`N`of`X`. This function is available under the name`BESYN`

as a GNU extension. If`N`and`X`are arrays, their ranks and shapes shall conform.`BESSEL_YN(N1, N2, X)`

returns an array with the Bessel functions of the first kind of the orders`N1`to`N2`.*Standard*:Fortran 2008 and later, negative

`N`is allowed as GNU extension*Class*:Elemental function, except for the transformational function

`BESSEL_YN(N1, N2, X)`

*Syntax*:`RESULT = BESSEL_YN(N, X)`

`RESULT = BESSEL_YN(N1, N2, X)`

*Arguments*:`N`Shall be a scalar or an array of type `INTEGER`

.`N1`Shall be a non-negative scalar of type `INTEGER`

.`N2`Shall be a non-negative scalar of type `INTEGER`

.`X`Shall be a scalar or an array of type `REAL`

; for`BESSEL_YN(N1, N2, X)`

it shall be scalar.*Return value*:The return value is a scalar of type

`REAL`

. It has the same kind as`X`.*Note*:The transformational function uses a recurrence algorithm which might, for some values of

`X`, lead to different results than calls to the elemental function.*Example*:program test_besyn real(8) :: x = 1.0_8 x = bessel_yn(5,x) end program test_besyn

*Specific names*:Name Argument Return type Standard `DBESYN(N,X)`

`INTEGER N`

`REAL(8)`

GNU extension `REAL(8) X`

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