SUM, ROUND, IF and the other functions of a table formula do most of the calculating in a table cell. The tables below list every function that TX Text Control evaluates in a table formula, with its arguments, the value an omitted argument takes and what the function returns. They apply to formulas that users enter on the Formulas tab of the ribbon, that your code sets with TableCell.Formula and that arrive with a loaded Excel worksheet.

Constants, operators, cell references and number formats are explained in Calculate With Formulas of Tables and Table Formulas.

How to Read the Tables

Office Open XML defines the functions (ISO/IEC 29500-1, section 18.17.7, Predefined Function Definitions), and that chapter gives their argument types, restrictions and return values in full. The signatures below use this notation:

Square brackets mark an optional argument: LOG(x[,base]) is called as LOG(100) or as LOG(8,2). The description says which value an omitted argument takes.
argument-list is one or more arguments separated by commas. Each one is a constant, a cell reference, a range such as A1:A3, an array constant such as {1,2,3} or the result of another function.
array and reference stand for a range or a single cell reference.
Function names are uppercase, and the parentheses are required even when there is no argument: PI().

TableCollection.SupportedFormulaFunctions returns the names of the supported functions at runtime.

Mathematical and Trigonometric Functions

Function	Description
`ABS(x)`	The absolute value of x.
`ACOS(x)`	The arc cosine of x.
`ACOSH(x)`	The inverse hyperbolic cosine of x.
`ASIN(x)`	The arc sine of x.
`ASINH(x)`	The inverse hyperbolic sine of x.
`ATAN(x)`	The arc tangent of x.
`ATAN2(x,y)`	The arc tangent of the coordinates x and y.
`ATANH(x)`	The inverse hyperbolic tangent of x.
`CEILING(x,significance)`	x rounded up, away from zero, to the nearest multiple of significance. Positive and negative values are both rounded away from zero.
`COMBIN(number,number-chosen)`	The number of groups of number-chosen objects that can be formed from number objects.
`COS(x)`	The cosine of x.
`COSH(x)`	The hyperbolic cosine of x.
`DEGREES(angle)`	angle converted from radians to degrees.
`ECMA.CEILING(x,significance)`	x rounded up, away from zero, to the nearest multiple of significance, the same as `CEILING`.
`EVEN(x)`	x rounded away from zero to the nearest even integer.
`EXP(x)`	e raised to the power of x, where e is the base of the natural logarithm.
`FACT(x)`	The factorial of x.
`FACTDOUBLE(n)`	The double factorial of n.
`FLOOR(x,significance)`	x rounded down, toward zero, to the nearest multiple of significance.
`GCD(argument-list)`	The greatest common divisor of one or more numbers.
`INT(x)`	x rounded down to an integer.
`ISO.CEILING(x[,significance])`	x rounded up to the nearest multiple of significance, whatever the sign of x. significance is 1 when it is omitted.
`LCM(argument-list)`	The least common multiple of one or more numbers.
`LN(x)`	The natural logarithm of x.
`LOG(x[,base])`	The logarithm of x to base. base is 10 when it is omitted.
`LOG10(x)`	The logarithm of x to base 10.
`MOD(x,y)`	The remainder of x divided by y. The result has the sign of y.
`MROUND(x,multiple)`	x rounded away from zero to a multiple of multiple. It rounds up when the remainder of x divided by multiple is at least half of multiple, and down otherwise.
`MULTINOMIAL(argument-list)`	The factorial of the sum of the values, divided by the product of their factorials.
`ODD(x)`	x rounded away from zero to the nearest odd integer.
`PI()`	The number π.
`POWER(x,y)`	x raised to the power of y.
`PRODUCT(argument-list)`	The product of the numeric values of the arguments.
`QUOTIENT(dividend,divisor)`	The integer part of dividend divided by divisor.
`RADIANS(angle)`	angle converted from degrees to radians.
`RAND()`	A random real number, evenly distributed, from 0 up to but not including 1.
`RANDBETWEEN(lower-bound,upper-bound)`	A random integer from lower-bound to upper-bound.
`ROUND(x,number-digits)`	x rounded to number-digits digits.
`ROUNDDOWN(x,number-digits)`	x rounded down, toward zero, to number-digits digits.
`ROUNDUP(x,number-digits)`	x rounded up, away from zero, to number-digits digits.
`SERIESSUM(input-value,initial-power,step,coefficients)`	The sum of a power series.
`SIGN(x)`	The sign of x.
`SIN(x)`	The sine of x.
`SINH(x)`	The hyperbolic sine of x.
`SQRT(x)`	The positive square root of x.
`SQRTPI(x)`	The positive square root of x multiplied by π.
`SUM(argument-list)`	The sum of the numeric values of the arguments.
`SUMSQ(argument-list)`	The sum of the squares of the arguments.
`SUMX2MY2(array-1,array-2)`	The sum of the differences of the squares of corresponding numbers in two arrays.
`SUMX2PY2(array-1,array-2)`	The sum of the sums of the squares of corresponding numbers in two arrays.
`SUMXMY2(array-1,array-2)`	The sum of the squares of the differences of corresponding numbers in two arrays.
`TAN(x)`	The tangent of x.
`TANH(x)`	The hyperbolic tangent of x.
`TRUNC(x[,number-digits])`	x truncated to number-digits decimal places.

Statistical Functions

Function	Description
`AVERAGE(argument-list)`	The arithmetic mean of the numeric values of the arguments.
`COUNT(argument-list)`	The number of arguments that are numbers, plus the number of referenced cells that contain numbers. Dates aren't counted.
`COUNTA(argument-list)`	The number of arguments that aren't cell references, plus the number of referenced cells that aren't empty. Dates in arrays and in referenced cells aren't counted.
`COUNTBLANK(cell-range)`	The number of empty cells in a range. A cell whose formula returns an empty string isn't counted.
`MAX(argument-list)`	The largest of a set of numbers.
`MAXA(argument-list)`	The largest of a set of numbers.
`MIN(argument-list)`	The smallest of a set of numbers.
`MINA(argument-list)`	The smallest of a set of numbers.

Logical Functions

Function	Description
`AND(argument-list)`	`TRUE` if all arguments are `TRUE`. All arguments are evaluated before the result is returned.
`FALSE()`	The value `FALSE`, the same as the logical constant `FALSE`.
`IF(logical-value,[value-if-true][,[value-if-false]])`	Evaluates and returns value-if-true when logical-value is `TRUE`, and value-if-false otherwise.
`NOT(logical-value)`	The logical negation of logical-value.
`OR(argument-list)`	`TRUE` if at least one argument is `TRUE`. All arguments are evaluated before the result is returned.
`TRUE()`	The value `TRUE`, the same as the logical constant `TRUE`.

Lookup and Reference Functions

Function	Description
`ADDRESS(row-number,col-number[,[ref-type][,[A1-ref-style-flag][,sheet-name]]])`	The address of the cell in row-number and col-number, as text.
`CHOOSE(index,argument-list)`	The argument of argument-list at position index.
`COLUMN([reference])`	The column number of reference. Without reference, the column of the cell that contains the formula.
`COLUMNS(array)`	The number of columns of array. Only cell references and ranges are supported as array.
`ROW([reference])`	The row number of reference. Without reference, the row of the cell that contains the formula.
`ROWS(array)`	The number of rows of array. Only cell references and ranges are supported as array.

Information Functions

Function	Description
`ISBLANK(value)`	Whether value refers to an empty cell.
`ISEVEN(value)`	Whether value is an even number or refers to a cell with an even number.
`ISLOGICAL(value)`	Whether value is a logical value or refers to a cell with a logical value.
`ISNONTEXT(value)`	Whether value isn't text and doesn't refer to a cell with text. An empty cell doesn't count as text.
`ISNUMBER(value)`	Whether value is a number or refers to a cell with a number.
`ISODD(value)`	Whether value is an odd number or refers to a cell with an odd number.
`ISREF(value)`	Whether value is a cell reference.
`ISTEXT(value)`	Whether value is text or refers to a cell with text.
`N(value)`	value converted to a number. For a reference to a single cell, the value of that cell converted to a number.
`NA()`	The error value `#N/A`. Writing `#N/A` in the formula has the same result.
`TYPE(value)`	The type of value. For a reference to a single cell, the type of the value in that cell.

Excel Functions in Loaded Worksheets

StreamType.SpreadsheetML loads a worksheet of an XLSX file as a table, as described in Supported File Formats. The formulas of the worksheet become table formulas, and TX Text Control calculates them with the functions of the tables above. Text Control's list of supported Excel functions names these:

Group	Functions
Mathematical and trigonometric	`ABS`, `ACOS`, `ACOSH`, `ASIN`, `ASINH`, `ATAN2`, `ATANH`, `CEILING`, `COMBIN`, `COS`, `COSH`, `DEGREES`, `ECMA.CEILING`, `EVEN`, `EXP`, `FACT`, `FACTDOUBLE`, `FLOOR`, `GCD`, `INT`, `ISO.CEILING`, `LCM`, `LN`, `LOG`, `LOG10`, `MOD`, `MROUND`, `ODD`, `PI`, `POWER`, `PRODUCT`, `QUOTIENT`, `RADIANS`, `RAND`, `RANDBETWEEN`, `ROUND`, `ROUNDDOWN`, `ROUNDUP`, `SIGN`, `SIN`, `SINH`, `SQRT`, `SQRTPI`, `SUM`, `SUMIF`, `TAN`, `TANH`
Statistical	`AVERAGE`, `AREAS`, `MAX`, `MAXA`, `MIN`, `MINA`
Lookup and reference	`ADDRESS`, `ROW`

The other functions of the tables above, such as ATAN, COUNT or AND, belong to the same set of table formula functions. Two names of the Excel list are not in the list of formula functions:

Function	Described as
`SUMIF`	Applies selection criteria to the values of one range of cells and adds up the values of the corresponding cells in another range
`AREAS`	The number of areas a reference designates

Before you rely on one of them, or on any function of a worksheet you load, check whether SupportedFormulaFunctions contains its name. The following handler in MainWindow.xaml.cs of a window with a TextControl named textControl1 shows the number of supported functions and whether SUMIF is one of them:

using System;
using System.Windows;

namespace SampleApp;

public partial class MainWindow : Window
{
    private void CheckFunctions_Click(object sender, RoutedEventArgs e)
    {
        // The names of all functions a table formula can call
        string[] functions = textControl1.Tables.SupportedFormulaFunctions;

        bool sumIf = Array.IndexOf(functions, "SUMIF") >= 0;

        MessageBox.Show($"{functions.Length} functions, SUMIF supported: {sumIf}");
    }
}

TextControl.Tables returns the TableCollection of the main text, and SupportedFormulaFunctions is a read-only array of function names.

Formula Functions