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A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
The factorial number system is a mixed radix numeral system: the i-th digit from the right has base i, which means that the digit must be strictly less than i, and that (taking into account the bases of the less significant digits) its value is to be multiplied by (i − 1)!
The full formula, together with precise estimates of its error, can be derived as follows. Instead of approximating !, one considers its natural logarithm, as this is a slowly varying function: (!) = + + + .
Here is a sample program that computes the factorial of an integer number from 2 to 69 (ignoring the calculator's built-in factorial/gamma function). There are two versions of the example: one for algebraic mode and one for RPN mode. The RPN version is significantly shorter. Algebraic version:
Dropping B results in a full factorial 2 3 design for the factors A, C, and D. Performing the anova using factors A, C, and D, and the interaction terms A:C and A:D, gives the results shown in the table, which are very similar to the results for the full factorial experiment experiment, but have the advantage of requiring only a half-fraction 8 ...
Factorial designs allow the effects of a factor to be estimated at several levels of the other factors, yielding conclusions that are valid over a range of experimental conditions. The main disadvantage of the full factorial design is its sample size requirement, which grows exponentially with the number of factors or inputs considered. [6]
Stirling numbers express coefficients in expansions of falling and rising factorials (also known as the Pochhammer symbol) as polynomials.. That is, the falling factorial, defined as = (+) , is a polynomial in x of degree n whose expansion is
Let be a natural number. For a base >, we define the sum of the factorials of the digits [5] [6] of , :, to be the following: = =!. where = ⌊ ⌋ + is the number of digits in the number in base , ! is the factorial of and