Built-In Functions

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) Base 10 Logarithm

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