Parser Functions
General Functions
^
Power
%
Modulus Division
!
Factorial (of Integer)
ABS(X)
Absolute Value
CEIL(X)
Integer Above X
EXP(X)
Exponential
FLOOR(X)
Integer Below X
FRACTION(X)
Fractional Part of X
INTEGER(X)
Integer Part of X
LN(X)
Natural Logarithm
LOG(X)
Natural Logarithm
LOG10(X)
Base 10l Logarithm
Since TableCurve 9, LOG is the natural logarithm (as in PeakLab, Maple and Mathematica); use LOG10 for base 10. Files from earlier versions are converted automatically when opened
PI
3.14159265358979323846
RAND(N)
Random Integer Between 0 and N Inclusive
RANDOM
Random Number Between 0 and 1 Inclusive
ROUND(X)
Round X to Nearest Integer
SQRT(X)
Square Root of X
Function Name Case Rules
The elementary functions above (ABS, SQRT, LN, LOG, LOG10, EXP, POW, MOD, the trig and hyperbolic functions including ATAN2, FRACTION, INTEGER, ROUND, FLOOR, CEIL, DTOR, RTOD) accept any case: atan, Atan and ATAN are the same function. Special and statistical functions (GAM, LNGAM, ERF, J0, JN, HYPF, and similar) and the classic model functions (GAUSS_, EMG_, and similar) are upper case, though many have Maple/Mathematica aliases (Gamma, Erf, and similar) that accept any case. An unknown function name is always reported as an error.
Conditional Expressions
IF(expr,n1,n2)
Evaluates to n1 if expr true, n2 if expr false
> .GT.
Greater
< .LT.
Less
>= .GE.
Greater or Equal
<= .LE.
Less or Equal
== .EQ.
Equal
<> .NE.
Not Equal
Trigonometric Functions
ACOS(X)
ArcCosine of X (radians)
ACOSH(X)
Hyperbolic ArcCosine
ASIN(X)
ArcSine of X (radians
ASINH(X)
Hyperbolic ArcSine
ATAN(X)
ArcTangent of X (radians)
ATAN2(X,Y)
ArcTangent of X/Y (radians)
ATANH(X)
Hyperbolic ArcTangent
COS(X)
Cosine of X radians
COSH(X)
Hyperbolic Cosine
COT(X)
Cotangent of X radians
COTH(X)
Hyperbolic Cotangent
CSC(X)
Cosecant of X radians
CSCH(X)
Hyperbolic Cosecant
DTOR(Deg)
Degrees to Radians
RTOD(Rad)
Radians to Degrees
SEC(X)
Secant of X radians
SECH(X)
Hyperbolic Secant
SIN(X)
Sine of X radians
SINH(X)
Hyperbolic Sine
TAN(X)
Tangent of X radians
TANH(X)
Hyperbolic Tangent
Statistical Functions
!
Factorial (of Integer)
B0(N)
Bernoulli Number B0(N)
BET(A,B)
Beta Function
ERF(X)
Error Function
ERFC(X)
Error Function, Complement
ERFP1(X)
Error Function + 1.0
ERFM1(X)
Error Function - 1.0
GAM(X)
Gamma Function
HYPM(A,B,X)
Hypergeometric M
HYPU(A,B,X)
Hypergeometric U
HYPF(A,B,C,X)
Hypergeometric F
IBETA(A,B,X)
Incomplete Beta Function
IGAM(A,X)
Incomplete Gamma
IGAMC(A,X)
Incomplete Gamma, Complement
LGNDR(L,M,X)
Legendre Polynomial PLM(X)
LNFAC(X)
Natural Logarithm Factorial
LNGAM(X)
Natural Logarithm Gamma
PFBI(K,N,P)
Binomial Probability (Probability >=K Occurrences in N trials, P=probability/trial)
PFCP(K,N)
Cumulative Poisson Probability (Probability 0 to K-1 Occurrences for Mean=N)
PFF(V1,V2,F)
F Probability (Probability Variance 1 >= Variance 2 for F=f-statistic, V1=DOF1,V2=DOF2)
PFST(T,V)
Student-t Probability (Probability t < Observed t for v=DOF)
PFX2(X2,V)
Chi-Squared Probability (Probability Observed C2 < C2 for v DOF)
PFX2C(X2,V)
Chi-Squared Complement Probability (Probability Observed C2 > C2 for v DOF)
PSI(X)
Psi (Digamma) Function
Bessel Functions
J0(X) J1(X) JN(N,X)
Integer Order J Bessel, orders 0, 1, N
Y0(X) Y1(X) YN(N,X)
Integer Order Y Bessel, orders 0, 1, N
I0(X) I1(X) IN(N,X)
Integer Order I Modified Bessel, orders 0, 1, N
I0EIX(X) I1EIX(X)
EXP(-X) * Integer Order I Modified Bessel, orders 0, 1
K0(X) K1(X) KN(N,X)
Integer Order K Modified Bessel, orders 0, 1, N
JNU(NU,X)
Fractional Order J Bessel
YNU(NU,X)
Fractional Order Y Bessel
INU(NU,X)
Fractional Order I Modified Bessel
KNU(NU,X)
Fractional Order K Modified Bessel
DJNU(NU,X)
Fractional Order J Bessel 1st Derivative
DYNU(NU,X)
Fractional Order Y Bessel 1st Derivative
DINU(NU,X)
Fractional Order I Modified Bessel 1st Derivative
DKNU(NU,X)
Fractional Order Modified K Bessel 1st Derivative
SPHJN(N,X)
Spherical Bessel j
SPHYN(N,X)
Spherical Bessel y
SPHIN(N,X)
Spherical Modified Bessel i
SPHKN(N,X)
Spherical Modified Bessel k
DSPHJN(N,X)
Spherical Bessel j 1st Derivative
DSPHYN(N,X)
Spherical Bessel y 1st Derivative
DSPHIN(N,X)
Spherical Modified Bessel i 1st Derivative
DSPHKN(N,X)
Spherical Modified Bessel k 1st Derivative
AIRYA(X)
Airy A Function
AIRYB(X)
Airy B Function
DAIRYA(X)
Airy A 1st Derivative
DAIRYB(X)
Airy B 1st Derivative
Integral, Derivative, and Summation Functions
DX(n)
1st Derivative of function Fn with respect to X, d(#Fn)/dX.
DX2(n)
2nd Derivative of function Fn with respect to X, d2(#Fn)/dX2.
DY(n)
1st Derivative of function Fn with respect to Y, d(#Fn)/dY.
DY2(n)
2nd Derivative of function Fn with respect to Y, d2(#Fn)/dX2.
DXY(n)
Derivative of function Fn with respect to X and Y, d(#Fn)/dXdY.
Derivative Examples:
AI(n,st,end)AIP(n,st,end,prec)
Automated Integration of Fn from st to end with $ as variable of integration; supports infinite limits
and undefined bounds; AI() seeks 1E-8 precision, AIP() seeks prec fractional convergence. The AI() and
AIP() functions first attempt to achieve the target precision with a successive step Gaussian Quadrature
procedure. If this is unsuccessful, a Romberg procedure with a maximum of 131K-177K steps follows.
QI(n,st,end)QIP(n,st,end,prec)
Gaussian Quadrature Integration of Fn from st to end with $ as variable of integration; supports infinite
limits and undefined bounds; QI() seeks 1E-8 precision, QIP() seeks prec fractional convergence.
Integration Example:
INF -INF
Infinite Limits for Integration functions. You should always use the INF constant rather than some
arbitrarily large number.
DQIP(n, ost, oend, ist, iend, prec)
Gaussian Quadrature Double Integration of Fn from st to end with $ as outer variable of integration
ranging from ost to oend and with $$ as the inner variable of integration ranging from ist to iend; supports
infinite limits and undefined bounds; seeks prec fractional convergence.
Double Integration Example:
SUM(n,st,end,inc)
Sums Fn with index $ going from st to end with increment inc
SER(n,st,inc,lim)
Sums Fn with index $ beginning at st, incrementing with inc, until iteration’s fractional contribution
lim
PROD(n,st,end,inc)
Multiplies Fn with index $ going from st to end with increment inc
XYZ Data Table Constants and Functions
XMIN
Minimum X
XMAX
Maximum X
XRANGE
Maximum X - Minimum X
XMN or XMEAN
Mean of X Values
XSTD
Standard deviation of X values
XATYMIN
X of X,Y,Z point having minimum Y
XATYMAX
X of X,Y,Z point having maximum Y
XATZMIN
X of X,Y,Z point having minimum Z
XATZMAX
X of X,Y,Z point having maximum Z
XATXYMIN
X of X,Y,Z point having minimum XY vector length
XATXYMAX
X of X,Y,Z point having maximum XY vector length
XATXYZMIN
X of X,Y,Z point having minimum XYZ vector length
XATXYZMAX
X of X,Y,Z point having maximum XYZ vector length
XATXMAXYMIN
X of X,Y,Z point nearest maximum X, minimum Y
XATXMNYMIN
X of X,Y,Z point nearest X mean, minimum Y
XATXMINYMIN
X of X,Y,Z point nearest minimum X, minimum Y
XATXMAXYMN
X of X,Y,Z point nearest maximum X, Y mean
XATXMNYMN
X of X,Y,Z point nearest X mean, Y mean
XATXMINYMN
X of X,Y,Z point nearest minimum X, Y mean
XATXMAXYMAX
X of X,Y,Z point nearest maximum X, maximum Y
XATXMNYMAX
X of X,Y,Z point nearest X mean, maximum Y
XATXMINYMAX
X of X,Y,Z point nearest minimum X, maximum Y
YMIN
Minimum Y
YMAX
Maximum Y
YRANGE
Maximum Y - Minimum Y
YMN or YMEAN
Mean of Y Values
YSTD
Standard deviation of Y values
YATXMIN
Y of X,Y,Z point having minimum X
YATXMAX
Y of X,Y,Z point having maximum X
YATZMIN
Y of X,Y,Z point having minimum Z
YATZMAX
Y of X,Y,Z point having maximum Z
YATXYMIN
Y of X,Y,Z point having minimum XY vector length
YATXYMAX
Y of X,Y,Z point having maximum XY vector length
YATXYZMIN
Y of X,Y,Z point having minimum XYZ vector length
YATXYZMAX
Y of X,Y,Z point having maximum XYZ vector length
YATXMAXYMIN
Y of X,Y,Z point nearest maximum X, minimum Y
YATXMNYMIN
Y of X,Y,Z point nearest X mean, minimum Y
YATXMINYMIN
Y of X,Y,Z point nearest minimum X, minimum Y
YATXMAXYMN
Y of X,Y,Z point nearest maximum X, Y mean
YATXMNYMN
Y of X,Y,Z point nearest X mean, Y mean
YATXMINYMN
Y of X,Y,Z point nearest minimum X, Y mean
YATXMAXYMAX
Y of X,Y,Z point nearest maximum X, maximum Y
YATXMNYMAX
Y of X,Y,Z point nearest X mean, maximum Y
YATXMINYMAX
Y of X,Y,Z point nearest minimum X, maximum Y
ZMIN
Minimum Z
ZMAX
Maximum Z
ZRANGE
Maximum Z - Minimum Z
ZMN or ZMEAN
Mean of Z Values
ZSTD
Standard deviation of Z values
ZATXMIN
Z of X,Y,Z point having minimum X
ZATXMAX
Z of X,Y,Z point having maximum X
ZATYMIN
Z of X,Y,Z point having minimum Y
ZATYMAX
Z of X,Y,Z point having maximum Y
ZATXYMIN
Z of X,Y,Z point having minimum XY vector length
ZATXYMAX
Z of X,Y,Z point having maximum XY vector length
ZATXYZMIN
Z of X,Y,Z point having minimum XYZ vector length
ZATXYZMAX
Z of X,Y,Z point having maximum XYZ vector length
ZATXMAXYMIN
Z of X,Y,Z point nearest maximum X, minimum Y
ZATXMNYMIN
Z of X,Y,Z point nearest X mean, minimum Y
ZATXMINYMIN
Z of X,Y,Z point nearest minimum X, minimum Y
ZATXMAXYMN
Z of X,Y,Z point nearest maximum X, Y mean
ZATXMNYMN
Z of X,Y,Z point nearest X mean, Y mean
ZATXMINYMN
Z of X,Y,Z point nearest minimum X, Y mean
ZATXMAXYMAX
Z of X,Y,Z point nearest maximum X, maximum Y
ZATXMNYMAX
Z of X,Y,Z point nearest X mean, maximum Y
ZATXMINYMAX
Z of X,Y,Z point nearest minimum X, maximum Y
NOISE(P)
Random Uniform P% Z Noise. A calculation Z=Z+NOISE(10) would be used to add 10% uniform random noise
to a data set.
GNOISE(P)
Random Gaussian P% Z Noise. A calculation Z=Z+GNOISE(10) would be used to add 10% Gaussian random
noise to a data set.
Non-Linear Base Functions
The non-linear base functions are built-in functions that enable fast and easy construction of UDFs and View Functions.
These functions are available in X, Y, and variable of integration $ versions. An X suffix processes the X variable, the Y suffix processes the Y variable, and the $ suffix processes the variable of integration.
The following abbreviations are used:
AMPL = Amplitude
CTR = Center
WID = Peak or Transition Width
RATE = Time Constant Term
The functions are as follows with the suffix X, Y, or $ to replace the _ symbol:
GAUSS_(AMPL, CTR, WID)
Gaussian Peak
LOR_(AMPL,CTR,WID)
Lorentzian Peak
LOGNORM_(AMPL,CTR,WID)
Log Normal Peak
LOGISTIC_(AMPL,CTR,WID)
Logistic Peak
EXTRVAL_(AMPL,CTR,WID)
Extreme Value Peak
GCUM_(AMPL,CTR,WID)
Gaussian Cumulative
LORCUM_(AMPL,CTR,WID)
Lorentzian Cumulative
LNCUM_(AMPL,CTR,WID)
Log-Normal Cumulative
SIG_(AMPL,CTR,WID)
Sigmoid Transition
EXVCUM_(AMPL,CTR,WID)
Extreme-Value Cumulative
LDR_(AMPL,CTR,WID)
Logistic Dose Response Transition
EXP_(AMPL,RATE)
Single Exponential
POW_(BASE,EXP)
Power
Maple and Mathematica Functions
The elementary functions above (ABS, SQRT, LN, LOG, EXP, POW, MOD, all trig and hyperbolic functions, FRACTION, INTEGER, ROUND, FLOOR, CEIL, DTOR, RTOD) accept any case: atan, Atan, and ATAN are the same function. The Maple and Mathematica names below also accept any case. Every Maple and Mathematica continuous real function is now available by name, in addition to TableCurve's own classic functions; the Paste Mathematica button in the View Function dialog also rewrites Mathematica's bracket syntax, argument order, and parameter-versus-modulus differences automatically when you paste.
erfi(x), Erfi(x) Imaginary error function, -i erf(i x).
InverseErf(y), InverseErfc(z) Inverse error function and inverse complementary error function.
dawson(x), DawsonF(x) Dawson's integral, exp(-x^2) times the integral of exp(t^2) from 0 to x.
Si(x), SinIntegral(x), Ci(x), CosIntegral(x), Shi(x), SinhIntegral(x), Chi(x), CoshIntegral(x) The sine, cosine, and hyperbolic sine and cosine integrals.
FresnelS(x), FresnelC(x) The Fresnel sine and cosine integrals, pi/2 normalization.
Zeta(s) The Riemann zeta function.
Zeta(s,a), HurwitzZeta(s,a) The Hurwitz zeta function.
polylog(n,x), PolyLog(n,x) The polylogarithm, integer n, real x <= 1.
dilog(x) The dilogarithm (Maple); dilog(x) = PolyLog(2,1-x) for x >= 0.
Psi(n,x), PolyGamma(n,x) The polygamma function, the n-th derivative of the digamma function.
EllipticK(k), EllipticE(k) Complete elliptic integrals of the first and second kind, argument is the modulus k.
EllipticF(z,k), EllipticE(z,k) Incomplete elliptic integrals of the first and second kind, Legendre algebraic form, z = sin(phi), modulus k.
JacobiSN(u,k), JacobiCN(u,k), JacobiDN(u,k) The Jacobi elliptic functions sn, cn, and dn, modulus k.
HermiteH(n,x) The physicists' Hermite polynomial, integer n >= 0.
LaguerreL(n,x), LaguerreL(n,a,x) The Laguerre and generalized (associated) Laguerre polynomials, integer n >= 0.
ChebyshevT(n,x), ChebyshevU(n,x) The Chebyshev polynomials of the first and second kind, integer n >= 0.
LegendreP(n,x), LegendreQ(n,x) The Legendre polynomials of the first and second kind, integer n >= 0, any x.
LegendreP(l,m,x) The associated Legendre function, with the Condon-Shortley phase; |x| <= 1.
JacobiP(n,a,b,x) The Jacobi polynomial, integer n >= 0.
GegenbauerC(n,a,x) The Gegenbauer (ultraspherical) polynomial, integer n >= 0.
StruveH(nu,x), StruveL(nu,x) The Struve function and modified Struve function.
Hypergeometric0F1(b,x) The confluent limit function 0F1(;b;x).
Hypergeometric1F1(a,b,x), KummerM(a,b,x) The Kummer confluent hypergeometric function M(a,b,x).
HypergeometricU(a,b,x), KummerU(a,b,x) The Tricomi confluent hypergeometric function U(a,b,x). Exact for b = a+1 and a = 0; other integer b is undefined.
Hypergeometric2F1(a,b,c,x) The Gauss hypergeometric function, for x < 1 (and x = 1 where it converges).
AiryAiPrime(x), AiryBiPrime(x) The derivatives of the Airy functions Ai and Bi.
BetaRegularized(x,a,b) The regularized incomplete beta function I_x(a,b), in Mathematica's argument order.
GammaRegularized(a,x), GammaRegularized(a,x0,x1) The regularized upper incomplete gamma function Q(a,x), and Q(a,x0) - Q(a,x1).
bernoulli(n), BernoulliB(n) The Bernoulli number B_n.
Log2(x) Base 2 logarithm.
ArcSec(x), ArcCsc(x), ArcCot(x), ArcSech(x), ArcCsch(x), ArcCoth(x) The inverse secant, cosecant, cotangent, and their hyperbolic forms (Maple spells these arcsec, arccsc, arccot, arcsech, arccsch, arccoth, all lower case).
csgn(x) Complex sign (Maple).
Gudermannian(x), InverseGudermannian(x) The Gudermannian function and its inverse.
Haversine(x), InverseHaversine(x) The haversine function, (1 - cos(x))/2, and its inverse.
Logistic(x), LogisticSigmoid(x) The logistic sigmoid function.
Dirac(x), DiracDelta(x) The pointwise indicator (1 at x = 0, else 0) — not a distribution; it integrates to 0.
piecewise(c1,v1,...,cN,vN[,default]) Maple piecewise function, 2 to 9 arguments. The first true condition wins; with no default, an unmatched case returns 0.
Conventions for Maple and Mathematica Users
Every probed Maple and Mathematica continuous real function is available. What remains is convention: argument order, modulus versus parameter, and branch or normalization choices, where the parser follows Maple and the Paste Mathematica button rewrites the Mathematica forms on paste.
ArcTan(y,x) y is first, as in Maple and C. Mathematica's ArcTan[x,y] is x first — Paste Mathematica swaps it.
ArcCot(x), arccot(x) Maple's branch, pi/2 - arctan(x), range (0,pi). Mathematica's ArcCot[x] = ArcTan[1/x] — Paste Mathematica rewrites it.
Log(x), log(x), LOG(x), ln(x) All natural logarithm. Log(b,x) is base-b (Mathematica's argument order); LOG10(x) is base 10.
EllipticK(k), EllipticE(k) The argument is the modulus k (Maple). Mathematica's EllipticK[m] uses m = k^2: write EllipticK(sqrt(m)); Paste Mathematica does this automatically.
EllipticF(z,k), EllipticE(z,k) Maple's algebraic form, z = sin(phi). Mathematica's EllipticF[phi,m] becomes EllipticF(sin(phi),sqrt(m)).
JacobiSN(u,k), JacobiCN(u,k), JacobiDN(u,k) Modulus k (Maple). Mathematica's JacobiSN[u,m] becomes JacobiSN(u,sqrt(m)).
Gamma(a,x) The non-regularized upper incomplete gamma function. GammaRegularized(a,x) is the regularized Q(a,x); IGAM and IGAMC are the same regularized functions under their classic TableCurve names.
BetaRegularized(x,a,b) Mathematica's argument order, x first. IBETA(a,b,x) is the same function in TableCurve's classic argument order.
LegendreP(l,m,x) The associated Legendre function, with the Condon-Shortley phase, as in Mathematica; |x| <= 1. LegendreP(n,x) accepts any x.
HermiteH, LaguerreL, ChebyshevT, ChebyshevU, LegendreP, LegendreQ, JacobiP, GegenbauerC Integer degree n >= 0 only; real-degree forms are not implemented.
Dirac(x), DiracDelta(x) The pointwise indicator, not a distribution — it integrates to 0.
Erfi(x), DawsonF(x), dawson(x) Erfi overflows past x = 26.6, as the underlying function does. Dawson's integral is finite everywhere.