Built-In Functions

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  TableCurve 2D offers extensive mathematical function support in its Generate Data, Calculation, View Function(X), and User-Defined Function options.

 Function Insert Help

 A special Function Insert help exists for accessing the various functions used within user entered numeric expressions. Click on the type of function you are seeking and then on the specific function of interest. The function is automatically inserted into the calculation, view function, or UDF at the current cursor position. You may need to modify the symbols used as arguments in the function to match the variable intended for the expression.

 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 10 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

ROUND(X) Round X to Nearest Integer

SQRT(X) Square Root of X

 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’s 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

 Derivatives

 DX(Fn) - 1st Derivative of function Fn, d(Fn)/dX. Derivative is always with respect to X. UDF Example (1st Derivative of Gaussian):

 F1=#A*EXP(-((X-#B)/#C)^2)

 Y=DX(F1)

 DX2(n) - 2nd Derivative of function #Fn, d2(#Fn)/dX2. Derivative is always with respect to X. UDF Example (2nd Derivative of Gaussian):

 F1=#A*EXP(-((X-#B)/#C)^2)

 Y=DX2(F1)

 Integrals

 AI(n,st,end) and 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. For compatibility with previous versions, less automated integration procedures are also supported:

 RI(n,st,end) - Romberg Integration

 QI(n,st,end) - Gaussian Quadrature Integration, 24 step

 QIN(n,st,end,nstep) - Gaussian Quadrature Integration, nstep steps (avl steps=4,6,8,10,12,16,20,24,32,40,48,64,80,128)

 QIP(n,st,end,prec) - Gaussian Quadrature Integration, prec fractional convergence

 UDF Example (Cumulative of Log-Normal):

 UPPER=40.0

 F1=LN($/#C)/#D

 F2=EXP(-0.5*F1*F1)

 F3=AIP(F2,X,UPPER,1e-4)

 Y=#A+#B*F3

 INF and -INF - Infinite Limits for Integration functions. You should always use the INF constant rather than some arbitrarily large number.

 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

 XY Data Table Constants And Functions

 XMIN Minimum X

 XMAX Maximum X

 XRANGE Max X - Min X

 XMEAN Mean X

 XSTD Std Deviation X

 XMED Median X

 XATYMIN X at Min Y

 XATYMAX X at Max Y

 YMIN Minimum Y

 YMAX Maximum Y

 YRANGE Max Y - Min Y

 YMEAN Mean Y

 YSTD Std Deviation Y

 YMED Median Y

 YATXMIN Y at Min X

 YATXMAX Y at Max X

 XCTR X at Peak Center (Peak Profiles Only)

 XL50 X at Half-Maxima Left (Peak Profiles Only)

 XR50 X at Half-Maxima Right (Peak Profiles Only)

 XW50 X Width at Half-Maxima (Peak Profiles Only)

 X50 X at Ymin+Yrange/2

 X25 X at Ymin+Yrange/4

 X75 X at Ymin+3*Yrange/4

 XWTR X transition width (X75-X25)

 XWL Wavelength (Waveform Profiles Only)

 XPH, XPH2 Phase for Sine Wave and Sine2 Wave (Waveform Profiles Only)

 XYCNT Active Data Point Count

 XYINDEX Position within XY Data Table

 NOISE(P) Random Uniform P% Y Noise. A calculation Y=Y+NOISE(10) adds 10% uniform random noise.

 GNOISE(P) Random Gaussian P% Y Noise. A calculation Y=Y+GNOISE(10) adds 10% Gaussian random noise.

 Non-Linear Functions

 Peak Functions

ADC_(A0,A1,A2,A3,A4) Asymmetric Double Gaussian Cumulative

 ADS_(A0,A1,A2,A3,A4) Asymmetric Double Sigmoidal Peak

 ASYMLGSTC_(A0,A1,A2,A3) Asymmetric Logistic Peak

 BETA_(A0,A1,A2,A3,A4) Beta Peak

 CHISQ_(A0,A1,A2,A3) Chi-Squared Distribution

 EQUILPK_(A0,A1,A2,A3,A4) Kinetic Intermediate w/Lag,Equilibrium

 EMAXPOWPK_(A0,A1,A2) Exp to Max w/Power Term Peak

 EMG_(A0,A1,A2,A3) Exponentially Modified Gaussian

 ERFCPK_(A0,A1,A2) Complementary Error Function Peak

 ERROR_(A0,A1,A2,A3) Error Distribution

 EXTRVAL_(A0,A1,A2) Extreme Value

 EXTRVAL4T_(A0,A1,A2,A3) Extreme Value, 4-parameter tailed

 EXTRVAL4F_(A0,A1,A2,A3) Extreme Value, 4-parameter fronted

 FVAR_(A0,A1,A2,A3,A4) F-Variance Distribution

 GAMMA_(A0,A1,A2,A3) Gamma Peak

 GAUSS_(A0,A1,A2) Gaussian

 GAUSSLORXP_(A0,A1,A2,A3) Gaussian-Lorentzian Cross Product

 GAUSSMOD_(A0,A1,A2,A3) Modified Gaussian

 GMG_(A0,A1,A2,A3) Half-Gaussian Modified Gaussian

 INTMEDPK_(A0,A1,A2,A3) Kinetic Intermediate w/Lag

 INVGAMMA_(A0,A1,A2,A3) Inverted Gamma Distribution

 LAPLACE_(A0,A1,A2) Laplace or Double-Sided Exponential

 LDRPK_(A0,A1,A2) Logistic Dose Response Derivative Peak

 LGSTCPOWPK_(A0,A1,A2,A3) Logistic w/Power Term Peak

 LOGISTIC_(A0,A1,A2) Logistic Peak

 LOGNORM_(A0,A1,A2) Log Normal

 LOGNORM4_(A0,A1,A2,A4) Log Normal, 4-parameter

 LORENTZ_(A0,A1,A2) Lorentzian

 PEARSON4_(A0,A1,A2,A3,A4) Pearson IV

 PEARSON7_(A0,A1,A2,A3) Pearson VII

 PULSE_(A0,A1,A2) Pulse Peak

 PULSEPOW_(A0,A1,A2,A3) Pulse w/Power Term Peak

 PULSEWID2_(A0,A1,A2,A3) Pulse w/Second Width Peak

 SDC_(A0,A1,A2,A3) Symmetric Double Gaussian Cumulative Peak

 SDS_(A0,A1,A2,A3) Symmetric Double Sigmoidal Peak

 STUDENT_(A0,A1,A2,A3) Student’s t Distribution

 WEIBULL_(A0,A1,A2,A3) Weibull Peak

 Transition Functions

 ASYMSIG_(A0,A1,A2,A3) Asymmetric Sigmoid

 ASYMSIGREV_(A0,A1,A2,A3) Asymmetric Sigmoid w/Reverse Asymmetry

 CASCADE_(A0,A1,A2,A3) Cascade Transition

 EMGCUM_(A0,A1,A2,A3) Exponentially Modified Gaussian Cumulative

 EXTRVALCUM_(A0,A1,A2) Extreme Value Cumulative

 GAUSSCUM_(A0,A1,A2) Gaussian Cumulative

 IMPULSE_(A0,A1,A2,A3,A4) Impulse Transition

 LDR_(A0,A1,A2) Logistic Dose Response

 LOGNORMCUM_(A0,A1,A2) Log Normal Cumulative

 LORENTZCUM_(A0,A1,A2) Lorentzian Cumulative

 PULSECUM_(A0,A1,A2) Pulse Cumulative

 PULSEPWCUM_(A0,A1,A2,A3) Pulse w/Power Term Cumulative

 SDSCUM_(A0,A1,A2,A3) Symmetric Double Sigmoid Cumulative

 SIGMOID_(A0,A1,A2) Sigmoidal

 WEIBULLCUM_(A0,A1,A2,A3) Weibull Cumulative

 Kinetic Decay

 DECAYPT5_(A0,A1) Half Order Decay

 DECAY1_(A0,A1) First Order Decay

 DECAY2_(A0,A1) Second Order Decay

 DECAY2HYP_(A0,A1) Second Order Decay, Hyperbolic Form

 DECAY3_(A0,A1) Third Order Decay

 DECAYN_(A0,A1,A2) Variable Order Decay

 DECAY1P2_(A0,A1,A2) Simultaneous First and Second Order Decay

 DECAYAB$C_(A0,A1,A2) Decay of A for A+B->C

 DECAY1S1_(A0,A1,A2,A3) Two Independent First Order Decays

 DECAY1S2_(A0,A1,A2,A3) Independent First and Second Order Decays

 DECAY2S2_(A0,A1,A2,A3) Two Independent Second Order Decays

 Kinetic Formation

 FORMPT5_(A0,A1) Half Order Formation

 FORM1_(A0,A1) First Order Formation

 FORM2_(A0,A1) Second Order Formation

 FORM2HYP_(A0,A1) Second Order Formation, Hyperbolic Form

 FORM3_(A0,A1) Third Order Formation

 FORMN_(A0,A1,A2) Variable Order Formation

 FORM1P2_(A0,A1,A2) Simultaneous First and Second Order Formation

 FORMSEQ_(A0,A1,A2) Sequential First Order Formation

 FORM1S1_(A0,A1,A2,A3) Two Independent First Order Formations

 FORM1S2_(A0,A1,A2,A3) Independent First and Second Order Formations

 FORM2S2_(A0,A1,A2,A3) Two Independent Second Order Formations

 Kinetic Complex

 EQUILRTA$B_(A0,A1,A2) Simple Equilibrium, Rate Form

 EQUILCNA$B_(A0,A1,A2) Simple Equilibrium, Concentration Form

 EQUILA$BC_(A0,A1,A2) Complex Equilibrium A=B+C

 EQUILAB$CD_(A0,A1,A2) Complex Equilibrium A+B=C+D

 EQUILA$B$C_(A0,A1,A2,A3) Intermediate Peak w/Equilibrium

 INTMED_(A0,A1,A2) Intermediate Peak

 Waveform Equations

 SINE_(A0,A1,A2) Sine Wave

 SINE2_(A0,A1,A2) Sine2 Wave

 General Equations

 POWER_(A0,A1) Simple Power

 EXP_(A0,A1) Simple Exponential

 PeakFit Functions

 The PeakFit functions are a set of special peak, transition, and waveform functions built into PeakFit. These are made available in TableCurve 2D for cross-compatibility. The following abbreviations are used:

 AMPL = Amplitude

 CTR = Center

 WID, WID1 = Peak or Transition Width

 WID2 = Second Peak Width

 WID3 = Third Peak Width

 RATE, RATE1, RATE2 = Time Constant Terms

 DIST = Chromatographic Distortion Parameter

 PHASE = Waveform Phase

 WL = Waveform Wavelength

 DAMP = Waveform Dampening Parameter

 The functions are as follows:

 GAUSS(AMPL, CTR, WID) Gaussian Peak

 LORENTZ(AMPL,CTR,WID) Lorentzian Peak

 PEARSON(AMPL,CTR,WID1,WID2) Pearson VII Peak

 VOIGT(AMPL,CTR,WID1,WID2) Voigt Peak

 GAUSSA(AREA,CTR,WID) Area Gaussian Peak

 EMG(AREA,CTR,WID,RATE) Exponentially-modified Gaussian Peak

 GIDDING(AREA,CTR,WID) Gidding Peak Equation

 HVL(AREA,CTR,WID,DIST) Haarhoff VanderLinde Peak

 NLC(AREA,CTR,WID,DIST) Non-Linear Chromatography Peak

 LOGNORM(AMPL,CTR,WID) Log Normal Peak

 DBLEXP(AMPL1,RATE1,AMPL2,RATE2) Double Exponential

 DBLSIG(AMPL,CTR,WID1,WID2) Symmetric Double Sigmoid Peak

 DBLCUM(AMPL,CTR,WID1,WID2) Symmetric Double Cumulative Peak

 ADBLSIG(AMPL,CTR,WID1,WID2,WID3) Asymmetric Double Sigmoid Peak

 ADBLCUM(AMPL,CTR,WID1,WID2,WID3) Asymmetric Double Cumulative Peak

 SINE(AMPL,PHASE,WL) Sine Wave

 SINESQ(AMPL,PHASE,WL) Sine Squared Wave

 SINEDAMP(AMPL,PHASE,WL,DAMP) Dampened Sine Wave

 EXTRVAL(AMPL,CTR,WID) Extreme Value Peak

 GAMMA(AMPL,CTR,WID1,WID2) Gamma Statistical Peak

 WEIBULL(AMPL,CTR,WID1,WID2) Weibull Statistical Peak

 BETA(AMPL,CTR,WID1,WID2,WID3) Beta Statistical Peak

 LOGISTIC(AMPL,CTR,WID) Logistic Peak

 ERFCPK(AMPL,CTR,WID) Error Function Peak

 SIG(AMPL,CTR,WID) Sigmoid Transition

 CUM(AMPL,CTR,WID) Gaussian Cumulative Transition

 REVSIG(AMPL,CTR,WID) Reverse Sigmoid Transition

 REVCUM(AMPL,CTR,WID) Reverse Cumulative Transition

 LDR(AMPL,CTR,WID) Logistic Dose Response Transition

 SGLEXP(AMPL,RATE) Single Exponential