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Manual Reference Pages  - erfc_scaled (3fortran)

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NAME

ERFC_SCALED(3) - [MATHEMATICS] Scaled complementary error function

SYNOPSIS

result = erfc_scaled(x)

         elemental real(kind=KIND) function erfc_scaled(x)

          real(kind=KIND),intent(in) :: x

CHARACTERISTICS

o	X is of type real of any valid kind
o	KIND is any kind valid for a real type
o	the result has the same characteristics as X

DESCRIPTION

ERFC_SCALED(3) computes the exponentially-scaled complementary error function of X:

$$ e^{x^2} \frac{2}{\sqrt{\pi}} \int_{x}^{\infty} e^{-t^2} dt. $$

erfc_scaled(x)=exp(x*x)erfc(x)

NOTE1

The complementary error function is asymptotic to exp(-X2)/(X/PI). As such it underflows at approximately X >= 9 when using ISO/IEC/IEEE 60559:2011 single precision arithmetic. The exponentially-scaled complementary error function is asymptotic to 1/(X PI). As such it does not underflow until X > HUGE (X)/PI.

OPTIONS

o	X the value to apply the ERFC function to

RESULT

The approximation to the exponentially-scaled complementary error function of X

EXAMPLES

Sample program:

    program demo_erfc_scaled
    implicit none
    real(kind(0.0d0)) :: x = 0.17d0
       x = erfc_scaled(x)
       print *, x
    end program demo_erfc_scaled

Results:

     >   0.833758302149981

STANDARD

Fortran 2008

SEE ALSO

ERF(3), EXP(3), ERFC(3)

Fortran intrinsic descriptions (license: MIT) @urbanjost

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Nemo Release 3.1

erfc_scaled (3fortran)

November 02, 2024

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