A growing list of functions that you can use in formulas and scripting...

 abs (x) – absolute value

 abs# (vector#) – absolute value of each element of vector#

 abs## (matrix##) – absolute value of each cell of matrix##

 appendFile (filePath$, ...) – write texts, numbers, vectors and so on at the end of an existing file (create such a file if it does not exist yet)

 appendFileLine (filePath$, ...) – write texts, numbers, vectors and so on, followed by a newline, at the end of an existing file (create such a file if it does not exist yet)

 appendInfo (...) – write texts, numbers, vectors and so on, to the Info window

 appendInfoLine (...) – write texts, numbers, vectors and so on, followed by a newline, to the Info window

 arccos (x) – inverse cosine

 arccos# (vector#) – inverse cosine of each element of vector#

 arccos## (matrix##) – inverse cosine of each cell of matrix##

 arccosh (x) – inverse hyperbolic cosine

 arccosh# (vector#) – inverse hyperbolic cosine of each element of vector#

 arccosh## (matrix##) – inverse hyperbolic cosine of each cell of matrix##

 arcsin (x) – inverse sine

 arcsin# (vector#) – inverse sine of each element of vector#

 arcsin## (matrix##) – inverse sine of each cell of matrix##

 arcsinh (x) – inverse hyperbolic sine

 arcsinh# (vector#) – inverse hyperbolic sine of each element of vector#

 arcsinh## (matrix##) – inverse hyperbolic sine of each cell of matrix##

 arctan (x) – inverse tangent

 arctan# (vector#) – inverse tangent of each element of vector#

 arctan## (matrix##) – inverse tangent of each cell of matrix##

 arctan2 (y, x) – argument angle

 arctanh (x) – inverse hyperbolic tangent

 arctanh# (vector#) – inverse hyperbolic tangent of each element of vector#

 arctanh## (matrix##) – inverse hyperbolic tangent of each cell of matrix##

 assert condition – condition checking

 asynchronous – let the script continue while the sound is playing

 backslashTrigraphsToUnicode$ (string$) – convert e.g. \ct to ɔ

 barkToHertz (x) – from Bark-rate to acoustic frequency

 besselI (n, x) – modified Bessel function of the first kind, I_n

 besselK (n, x) – modified Bessel function of the second kind, K_n

 beta (x, y) – β function

 between_by# (low, high, step) – symmetrically dispersed numbers between low and high, in steps of step

 between_count# (low, high, n) – n symmetrically dispersed numbers between low and high (bin centres)

 binomialP (p, k, n) – probability of Bernoulli event occurring at most k in n times

 binomialQ (p, k, n) – probability of Bernoulli event occurring at least k in n times

 ceiling (x) – round up to integer

 ceiling# (vector#) – round up each element of vector#

 ceiling## (matrix##) – round up each cell of matrix##

 center (v#) – center (or centre) of gravity

 chiSquareP (chiSquare, df) – area under the χ² curve up to chiSquare

 chiSquareQ (chiSquare, df) – area under the χ² curve after chiSquare

 chooseFolder$ (title$) – pops up a folder selection window

 chooseReadFile$ (title$) – pops up a file selection window for opening (or appending to) an existing file

 chooseWriteFile$ (title$, defaultFilename$) – pops up a file selection window for saving to a new file

 clearinfo – clear the Info window

 columnSums# (matrix##)

 correlation (u#, v#) – correlation (between −1 and +1) of two vectors

 cos (x) – cosine

 cos# (vector#) – cosine of each element of vector#

 cos## (matrix##) – cosine of each cell of matrix##

 cosh (x) – hyperbolic cosine

 cosh# (vector#) – hyperbolic cosine of each element of vector#

 cosh## (matrix##) – hyperbolic cosine of each cell of matrix##

 createFolder (folderPath$) – create a new folder, or do nothing if it already exists

 date$ ( ) – current local date and time in the form "Mon Nov 8 16:32:42 2021"

 date_iso$ ( ) – current local date and time in the form "2021-11-08T16:32:42+01:00"

 date# ( ) – current local date and time in the form { 2021, 11, 8, 16, 32, 42 }

 date_utc$ ( ) – current standard date and time in the form "Mon Nov 8 15:32:42 2021"

 date_utc_iso$ ( ) – current standard date and time in the form "2021-11-08T15:32:42Z"

 date_utc# ( ) – current standard date and time in the form { 2021, 11, 8, 15, 32, 42 }

 deleteFile (filePath$) – delete a file, or do nothing if it does not exist

 demo – execute a graphics command in the Demo window (instead of in the Picture window)

 demoClicked ( ) – determine whether the user clicked in the Demo window

 demoClickedIn (xmin, xmax, ymmin, ymax) – determine whether the user clicked in a rectangular region in the Demo window

 demoCommandKeyPressed ( ) – determine whether the user pressed the Command key when they typed into the Demo window

 demoInput (characters$) – determine whether the user typed (or clicked) the specified characters into the Demo window

 demoKey$ ( ) – determine the key that the user typed into the Demo window

 demoKeyPressed ( ) – determine whether the user typed anything into the Demo window

 demoOptionKeyPressed ( ) – determine whether the user pressed the Option key when they typed into the Demo window

 demoPeekInput ( ) – see whether a user event (click or key press) is available in the Demo window

 demoShiftKeyPressed ( ) – determine whether the user pressed the Shift key when they typed into the Demo window

 demoShow ( ) – make all deferred drawing commands immediately visible

 demoWaitForInput ( ) – wait for a user event (click or key press) in the Demo window

 demoWindowTitle (newTitle$) – change the title of the Demo window

 demoX ( ) – the horizontal position of a mouse click in the Demo window

 demoY ( ) – the vertical position of a mouse click in the Demo window

 differenceLimensToPhon (x) – from jnd-scale to perceptual loudness

 editor (editor($)) – enter the environment of an editor (by number or by name)

 empty$# (numberOfStrings) – create an array of empty strings

 endeditor – leave the environment of an editor

 endproc – end a procedure definition

 endsWith (string$, part$) – determine whether string$ ends in part$

 environment$ (string$) – look up a system environment string

 erb (f) – equivalent rectangular bandwidth for frequency f

 erbToHertz (x) – from ERB-rate to acoustic frequency

 erf (x) – error function, the integral of the Gaussian

 erfc (x) – complement of the error function, i.e. 1 − erf (x); this is a separate function because erf (x) can be close to 1

 exitScript (...) – show a message that tells the user why the script will be interrupted

 exp (x) – exponentiation, i.e. e^x

 exp# (vector#) – exponentiate each element of vector#

 exp## (matrix##) – exponentiate each cell of matrix##

 extractLine$ (string$, part$) – everything that comes after the first occurrence of part$ in string$

 extractNumber (string$, part$) – the first number after the first occurrence of part$% in %string

 extractWord$ (string$, part$) – the first “word” after the first occurrence of part$% in %string

 fileNames$# (folderNameOrPattern$) – get the names (not the whole paths) of the files in a folder or that match a pattern with an asterisk

 fileReadable (filePath$) – 1 if the file exists and can be read, 0 otherwise

 fisherP (f, df1, df2) – area under the Fisher F curve up to f

 fisherQ (f, df1, df2) – area under the Fisher F curve after f

 fixed$ (number, precision) – format a number as a string, with precision digits after the decimal point

 floor (x) – round down to integer

 floor# (vector#) – round down each element of vector#

 floor## (matrix##) – round down each cell of matrix##

 folderNames$# (folderNameOrPattern$) – get the names (not the whole paths) of the subfolders in a folder or that match a pattern with an asterisk

 from_to# (m, n) – the integers from m through n

 from_to_by# (m, n, step) – numbers from m through n, in steps of step

 from_to_count# (start, end, n) – n numbers from start through end

 gaussP (z) – area under the normal curve up to z

 gaussQ (z) – area under the normal curve after z

 goto – place in a script to jump from

 hertzToBark (x) – from acoustic frequency to Bark-rate

 hertzToErb (x) – from acoustic frequency to ERB-rate

 hertzToMel (x) – from acoustic frequency to mel

 hertzToSemitones (x) – from acoustic frequency to logarithmic scale re 100 Hz

 imax (x, ...) – location of the maximum

 imin (x, ...) – location of the minimum

 index (string$, part$) – look up a substring, or 0 if not found

 index (strings$#, s$) – look up whether and where s$ first occurs in strings$

 index_regex (string$, regex$) – determine whether and where string$ first matches regex$

 inner (a#, b#) – inner product

 invBinomialP (P, k, n) – inverse of binomialP

 invBinomialQ (Q, k, n) – inverse of binomialQ

 invChiSquareQ (q, df) – inverse of chiSquareQ

 invFisherQ (q, df1, df2) – inverse of fisherQ

 invGaussQ (z) – inverse of gaussQ

 invSigmoid (x) – inverse sigmoid

 invSigmoid# (vector#) – inverse sigmoid of each element of vector#

 invSigmoid## (matrix##) – inverse sigmoid of each cell of matrix##

 invStudentQ (q, df) – inverse studentQ

 label – place in a script to jump to

 left$ (string$, n) – the n first characters in string$

 length (string$) – number of Unicode characters in string$

 ln (x) – natural logarithm, base e

 ln# (vector#) – natural logarithm of each element of vector#

 ln## (matrix##) – natural logarithm of each cell of matrix##

 lnGamma (x) – logarithm of the Γ function

 log2 (x) – logarithm, base 2

 log2# (vector#) – base-2 logarithm of each element of vector#

 log2## (matrix##) – base-2 logarithm of each cell of matrix##

 log10 (x) – logarithm, base 10

 log10# (vector#) – base-10 logarithm of each element of vector#

 log10## (matrix##) – base-10 logarithm of each cell of matrix##

 max (x, ...) – maximum

 mean (v#) – average of the elements of a vector

 melToHertz (x) – from mel to acoustic frequency

 mid$ (string$, from, n) – the n characters in string$ starting at position from

 min (x, ...) – minimum

 minusObject (...) – shrink the selection of objects in the list

 mul## (a##, b##) – matrix multiplication

 number (a$) – interpret a string as a number

 number# (a$#) – interpret strings as numbers

 numberOfColumns (matrix##)

 numberOfRows (matrix##)

 outer## (a#, b#) – outer product, i.e. result_ij = a_ib_j

 pauseScript (...) – show a message in a simple pause window

 percent$ (number, precision) – format a number as a string, with a trailing percent sign and precision digits after the decimal point

 phonToDifferenceLimens (x) – from perceptual loudness to jnd-scale

 plusObject (...) – extend the selection of objects in the list

 procedure: procedureName, ... – start a procedure definition

 randomBernoulli (p) – Bernoulli-distributed random deviate (0 or 1)

 randomBernoulli# (n, p) – n independent Bernoulli-distributed zeroes and ones

 randomGamma (shape, rate) – gamma-distributed random deviate

 randomGamma# (n, shape, rate) – n independent gamma-distributed random numbers

 randomGamma# (vector#, shape, rate) – duplicate vector#, and replace all elements with independent gamma-distributed random numbers

 randomGamma## (nrow, ncol, shape, rate) – nrow × ncol independent gamma-distributed random numbers

 randomGamma## (matrix##, shape, rate) – duplicate matrix##, and replace all cells with independent gamma-distributed random numbers

 randomGauss (mu, sigma) – normally distributed random deviate

 randomGauss# (n, mu, sigma) – n independent normally distributed random numbers

 randomGauss# (vector#, mu, sigma) – duplicate vector#, and replace all elements with independent normally distributed random numbers

 randomGauss## (nrow, ncol, mu, sigma) – nrow × ncol independent normally distributed random numbers

 randomGauss## (matrix##, mu, sigma) – duplicate matrix##, and replace all cells with independent normally distributed random numbers

 randomInteger (min, max) – uniformly distributed integer random deviate

 randomInteger# (n, min, max) – n independent uniformly distributed random integers

 randomInteger# (vector#, min, max) – duplicate vector#, and replace all elements with independent uniformly distributed random integers

 randomInteger## (nrow, ncol, min, max) – nrow × ncol independent uniformly distributed random integers

 randomInteger## (matrix##, min, max) – duplicate matrix##, and replace all cells with independent uniformly distributed random integers

 randomPoisson (mean) – Poisson-distributed random deviate

 randomPoisson# (n, mean) – n independent Poisson-distributed random numbers

 randomPoisson# (vector#, mean) – duplicate vector#, and replace all elements with independent Poisson-distributed random numbers

 randomPoisson## (nrow, ncol, mean) – nrow × ncol independent Poisson-distributed random numbers

 randomPoisson## (matrix##, mean) – duplicate matrix##, and replace all cells with independent Poisson-distributed random numbers

 randomUniform (min, max) – uniformly distributed random deviate

 randomUniform# (n, min, max) – n independent uniformly distributed random numbers

 randomUniform# (vector#, min, max) – duplicate vector#, and replace all elements with independent uniformly distributed random numbers

 randomUniform## (nrow, ncol, min, max) – nrow × ncol independent uniformly distributed random numbers

 randomUniform## (matrix##, min, max) – duplicate matrix##, and replace all cells with independent uniformly distributed random numbers

 random_initializeSafelyAndUnpredictably ( ) – undoes the effects of the following function

 random_initializeWithSeedUnsafelyButPredictably (seed) – reproducible sequence of random numbers

 readFile (filePath$) – read a number from a text file

 readFile$ (filePath$) – read a whole text file into a string

 readFile# (filePath$) – read a vector from a text file

 readFile## (filePath$) – read a matrix from a text file

 readLinesFromFile$# (filePath$) – read all lines from a text file

 rectify (x) – set to zero if negative (no change if positive)

 rectify# (vector#) – rectify each element of vector#

 rectify## (matrix##) – rectify each cell of matrix##

 removeObject (...) – remove objects from the list, by ID and/or name

 repeat# (v#, n) – repeat the whole sequence of elements of v# n times

 replace$ (a$, b$, c$, n) – within a$, replace the first n occurrences of b$ with c$, or all if n = 0

 replace_regex$ (a$, b$, c$, n) – within a$, replace the first n matches of regular expression b$ with the regular expression c$, or all if n = 0

 right$ (string$, n) – the n last characters in string$

 rindex (string$, part$) – look up a substring from the end, or 0 if not found

 rindex (strings$#, s$) – look up whether and where s$ last occurs in strings$#

 rindex_regex (string$, regex$) – determine whether and where string$ last matches regex$

 round (x) – nearest integer

 round# (vector#) – nearest integer of each element of vector#

 round## (matrix##) – nearest integer of each cell of matrix##

 rowSums# (matrix##)

 runScript (filePath$, ...) – run a script with the given arguments

 runSubprocess (executableFilePath$, ...) – run an external program with the given arguments

 runSubprocess$ (executableFilePath$, ...) – run an external program with the given arguments, and return its output

 runSystem (...) – run a system command line with the given arguments concatenated

 runSystem$ (...) – run a system command line with the given arguments concatenated, and return its output

 selected# ( ) – the IDs of all selected objects

 selected# (type) – the IDs of all selected objects of type type

 selected$# ( ) – the names of all selected objects

 selected$# (type) – the names of all selected objects of type type

 selectObject (...) – select objects in the list by ID and/or name

 semitonesToHertz (x) – from logarithmic scale re 100 Hz to acoustic frequency

 sigmoid (x) – 1 / (1 + e^-x)

 sigmoid# (vector#) – sigmoid of each element of vector#

 sigmoid## (matrix##) – sigmoid of each cell of matrix##

 sin (x) – sine

 sin# (vector#) – sine of each element of vector#

 sin## (matrix##) – sine of each cell of matrix##

 sinc (x) – sinus cardinalis: sin (x) / x

 sincpi (x) – sin (πx) / (πx)

 sinh (x) – hyperbolic sine

 sinh# (vector#) – hyperbolic sine of each element of vector#

 sinh## (matrix##) – hyperbolic sine of each cell of matrix##

 size (v#) – number of elements

 shuffle# (vector#) – randomize order

 shuffle$# (stringVector$#) – randomize order

 sleep (duration) – pause script for duration seconds

 softmax# (vector#)

 softmaxPerRow## (matrix##)

 solve# (a##, y#) – find x for which A · x = y

 solve## (a##, y##) – find X for which A · X = Y

 solveNonnegative# (a##, y# [, x], maximumNumberOfIterations, tolerance, infoLevel)

 solveSparse# (a##, y# [, x], maximumNumberOfNonzeros, maximumNumberOfIterations, tolerance, infoLevel)

 solveWeaklyConstrained# (a##, y#, alpha, delta)

 sort# (vector#) – reshuffle in increasing order

 sort$# (stringVector$#) – reshuffle in Unicode-alphabetical order

 sort_numberAware$# (stringVector$#) – reshuffle in Unicode-alphabetical order, with special attention to numbers

 splitByWhitespace$# (string$) – split a string into inks

 sqrt (x) – square root

 sqrt# (vector#) – square root of each element of vector#

 sqrt## (matrix##) – square root of each cell of matrix##

 startsWith (string$, part$) – determine whether string$ starts with part$

 stdev (v#) – standard deviation of the elements of a vector

 stopwatch – give the current value of the timer, which is then immediately reset to zero (note: no parentheses)

 string$ (number) – format a number as a string

 studentP (t, df) – area under the Student T curve up to t

 studentQ (t, df) – area under the Student T curve after t

 sum (v#) – sum the elements

 sumOver (loopVariable to n, numericExpressionOptionallyUsingLoopVariable) – Σ

 tan (x) – tangent

 tan# (vector#) – tangent of each element of vector#

 tan## (matrix##) – tangent of each cell of matrix##

 tanh (x) – hyperbolic tangent

 tanh# (vector#) – hyperbolic tangent of each element of vector#

 tanh## (matrix##) – hyperbolic tangent of each cell of matrix##

 to# (n) – the integers 1 through n

 transpose## (matrix##) – flip matrix along its diagonal

 tryToAppendFile (filePath$) – check whether a file can be appended to

 tryToWriteFile (filePath$) – check whether a file can be written (destructive!)

 unicode (c$) – the Unicode codepoint number that corresponds to character c$

 unicode$ (n) – the character that corresponds to Unicode codepoint n

 unicodeToBackslashTrigraphs$ (string$) – convert e.g. ɔ to \ct

 variableExists (variableName$) – does the variable variableName$ exist?

 vertical$ (stringArray$#) – format a string array vertically

 writeFile (filePath$, ...) – create a new text file, and write texts, numbers, vectors and so on into it

 writeFileLine (filePath$, ...) – create a new text file, write texts, numbers, vectors and so on into it, followed by a newline

 writeInfo (...) – write texts, numbers, vectors and so on, to a clear Info window

 writeInfoLine (...) – write texts, numbers, vectors and so on, followed by a newline, to a clear Info window

 zero# (n) – vector with n elements that are all 0

 zero## (nrow, ncol) – matrix with nrow × ncol elements that are all 0