# 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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