FM Function Domains

Dr. David M. Smith
Professor of Mathematics (Emeritus)
Loyola Marymount University
Los Angeles, CA



Here are the domains for the real functions supported in FM.


  abs(x)   all reals  
  acos(x)   -1 <= x <= 1  
  acosh(x)   1 <= x  
  asin(x)   -1 <= x <= 1  
  asinh(x)   all reals  
  atan(x)   all reals  
  atan2(x,y)   x, y: all reals  
  atanh(x)   -1 < x < 1  
  bessel_j0(x)   all reals  
  bessel_j1(x)   all reals  
  bessel_jn(n,x)   n >= 0 integer, x: all reals  
  bessel_jn(n1,n2,x)   n2 >= n1 >= 0 integer, x: all reals  
  bessel_y0(x)   x > 0  
  bessel_y1(x)   x > 0  
  bessel_yn(n,x)   n >= 0 integer, x: x > 0  
  bessel_yn(n1,n2,x)   n2 >= n1 >= 0 integer, x: x > 0  
  beta(x,y)   x, y: all reals except integers <= 0  
  binomial(x,y)   x, y: all reals except integers < 0  
  ceiling(x)   all reals  
  cos(x)   all reals  
  cosh(x)   all reals  
  cos_integral(x)   x > 0  
  cosh_integral(x)   x > 0  
  erf(x)   all reals  
  erfc(x)   all reals  
  erfc_scaled(x)   all reals  
  exp(x)   all reals  
  exp_integral_ei(x)   all non-zero x  
  exp_integral_en(n,x)   n < 1 integer, x: non-zero  
    n = 1 integer, x > 0  
    n > 1 integer, x >= 0  
  factorial(x)   all reals except integers < 0  
  fresnel_c(x)   all reals  
  fresnel_s(x)   all reals  
  floor(x)   all reals  
  gamma(x)   all reals except integers <= 0  
  hypot(x,y)   x, y: all reals  
  incomplete_beta(x,a,b)   0 <= x <= 1, a > 0, b >= 0  
  incomplete_gamma1(x,y)   x: all reals except integers <= 0, y >= 0  
  incomplete_gamma2(x,y)   x: all reals, y >= 0  
  int(x)   all reals  
  log(x)   x > 0  
  log10(x)   x > 0  
  log_erfc(x)   all reals  
  log_gamma(x)   x >= 0 or -2k < x < -2k+1  
  log_integral(x)   0 <= x < 1 or 1 < x  
  max(x,y,...)   2 to 10 arguments: all reals  
  min(x,y,...)   2 to 10 arguments: all reals  
  mod(x,y)   x: all reals, y: nonzero  
  modulo(x,y)   x: all reals, y: nonzero  
  nearest(x,y)   x, y: all reals  
  nint(x)   all reals  
  norm2(a)   array a: all reals  
  polygamma(n,x)   n >= 0 integer, x: all reals except integers <= 0  
  pochhammer(x,n)   n integer, x: all reals  
  psi(x)   all reals except integers <= 0  
  sign(x,y)   x, y: all reals  
  sin(x)   all reals  
  sin_integral(x)   all reals  
  sinh_integral(x)   all reals  
  sinh(x)   all reals  
  sqrt(x)   x >= 0  
  tan(x)   all reals  
  tanh(x)   all reals  



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