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)

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##

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##

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

columnSums# (matrix##)

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# ( ) – 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# ( ) – 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

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

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

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

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

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

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

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

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

numberOfColumns (matrix##)

numberOfRows (matrix##)

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

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

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 (μ, σ) – normally distributed random deviate

randomGauss# (n, μ, σ) – n independent normally distributed random numbers

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

randomGauss## (nrow, ncol, μ, σ) – nrow × ncol independent normally distributed random numbers

randomGauss# (matrix##, μ, σ) – 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

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

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##

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_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##)

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

softmax# (vector#)

softmaxPerRow## (matrix##)

sort# (vector#) – reshuffle in increasing order

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##)

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

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

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