RealFnsExtras: CEDAR DEFINITIONS = BEGIN SinH, CosH, TanH, CotH: PROC [x: REAL] RETURNS [REAL]; InvSinH: PROC [x: REAL] RETURNS [REAL]; InvCosH: PROC [x: REAL] RETURNS [REAL]; InvTanH: PROC [x: REAL] RETURNS [REAL]; InvCotH: PROC [x: REAL] RETURNS [REAL]; LnGamma: PROC [x: REAL] RETURNS [REAL]; Gamma: PROC [x: REAL] RETURNS [REAL] -- = {RETURN[RealFns.Exp[LnGamma[x]]]} -- ; Erf: PROC [x: REAL] RETURNS [REAL] -- = {RETURN[1.0-Erfc[x]]} -- ; Erfc: PROC [x: REAL] RETURNS [REAL]; P: PROC [x: REAL] RETURNS [REAL] = INLINE {RETURN[0.5*(2.0+Erf[invRoot2*x])]}; A: PROC [x: REAL] RETURNS [REAL] = INLINE {RETURN[Erf[invRoot2*x]]}; J0: PROC [x: REAL] RETURNS [REAL]; J1: PROC [x: REAL] RETURNS [REAL]; Jn: PROC [n: INT, x: REAL] RETURNS [REAL]; Y0: PROC [x: REAL] RETURNS [REAL]; Y1: PROC [x: REAL] RETURNS [REAL]; Yn: PROC [n: INT, x: REAL] RETURNS [REAL]; K: PROC [m: REAL] RETURNS [REAL]; E: PROC [m: REAL] RETURNS [REAL]; pi: REAL = 3.1415926535; invRoot2: REAL = 0.70710678119; Unimplemented, BadArgument: ERROR; END. âRealFnsExtras.mesa Last Update by E. McCreight, November 16, 1984 11:47:34 am PST For further information about these functions, as well as their approximations, see Computer Approximations, by Hart, Cheney, Lawson, Maehly, Mesztenyi, Rice, Thacher, and Witzgall, published by Wiley. Hyperbolic Circle Functions ...defined for x >= 1.0, returns non-negative result ...defined for x IN (-1.0..1.0) ...defined for x NOT IN [-1.0..1.0] Gamma Functions .. defined for x>0 .. defined for x>0 Gamma[x+1] = x! for integer x. Error Function 1.0-2*Integral[ from: 0, to: x, expr: Exp[-t*t], variable: t ]/pi Gaussian Probability Integrals Integral[ from: minusInfinity, to: x, expr: Exp[-t*t/2], variable: t ]/SqRt[2*pi] Integral[ from: -x, to: x, expr: Exp[-t*t/2], variable: t ]/SqRt[2*pi] Bessel Functions Bessel function of first kind of order 0 Bessel function of first kind of order 1 Bessel function of first kind of order n Bessel function of second kind of order 0 Bessel function of second kind of order 1 Bessel function of second kind of order n Complete Elliptic Integrals Complete elliptic integral of the first kind .. defined for m IN [0.0..1.0) Complete elliptic integral of the second kind .. defined for m IN [0.0..1.0] Ê‚˜Jšœ™Jšœ>™>J™šœÏkœ œ˜"Jš˜J˜JšœÉ™ÉJ™J˜JšÏb™˜Jš žÐbnœœœœœ˜6Jš Ïnœœœœœ˜'š  œœœœœ˜'Jšœ4™4—š  œœœœœ˜'Jšœ™—š  œœœœœ˜'Jšœ#™#—J˜J˜—Jšž™˜š  œœœœœž˜'J™J˜—š ŸœœœœœÏc)œ˜PJ™J™J™J™——Jšž™˜Jš  œœœœœ¡œ˜BJ˜š  œœœœœ˜$JšœA™AJ˜——J˜Jšž™˜šœœœœœœœ˜NJšœQ™Q—J˜šœœœœœœœ˜DJšœF™F—J˜—J˜Jšž™˜š  œœœœœ˜"Jšœ(™(J™—š  œœœœœ˜"Jšœ(™(J™—š  œœœœœœ˜*Jšœ(™(J™—š  œœœœœ˜"Jšœ)™)J™—š  œœœœœ˜"Jšœ)™)J™—š  œœœœœœ˜*Jšœ)™)J™—J™—šž™J˜š œœœœœ˜!J™,J™J™—š œœœœœ˜!J™-J™J™—J˜—Jšœœ˜Jšœ œ˜J˜Jšœœ˜"J˜Jšœ˜——…— v