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SINH(value) TANH Hyperbolic tangent. TANH(value) Using mathematical functions ALOG Antilogarithm (exponential). This is more accurate than 10^x due to limitations of the power function. ALOG(value) x EXP Natural exponential. This is more accurate than e due to limitations of the power function. EXP(value) EXPM1 Exponent minus 1 : ex–1. This is more accurate than EXP when x is close to zero. EXPM1(value) LNP1 Natural log plus 1 : ln(x+1). This is more accurate than the natural logarithm function when x is close to zero. LNP1(value) List functions These functions work on list data. See “List functions” on page 13-7. Using mathematical functions Loop functions The loop functions display a result after evaluating an expression a given number of times. ITERATE Repeatedly for #times evaluates an expression in terms of variable. The value for variable is updated each time, starting with initialvalue. ITERATE(expression,variable,initialvalue, #times) Example ITERATE(X2,X,2,3) returns 256 RECURSE Provides a method of defining a sequence without using the Symbolic view of the Sequence aplet. If used with | (“where”), RECURSE will step through the evaluation. RECURSE(sequencename,term-n,term1,term2) Example RECURSE(U,U(N-1)*N,1,2)672?_U1(N) Stores a factorial–calculating function named U1. When you enter U1(5), for example, the function calculates 5! (120). S Summation. Finds the sum of expression with respect to variable from initialvalue to finalvalue. S (variable=initialvalue,finalvalue,expression) Example S (C=1,5,C2) returns 55. Matrix functions These functions are for matrix data stored in matrix variables. See “Matrix functions and commands” on page 12-9. Using mathematical functions Polynomial functions Polynomials are products of constants (coefficients) and variables raised to powers (terms). POLYCOEF Polynomial coefficients. Returns the coefficients of the polynomial with the specified roots. POLYCOEF([roots]) Example To find the polynomial with roots 2, –3, 4, –5: POLYCOEF([2,-3,4,-5]) returns[1,2,-25, -26,120], representing x4+2x3–25x2–26x+120. POLYEVAL Polynomial evaluation. Evaluates a polynomial with the specified coefficients for the value of x. POLYEVAL([coefficients],value) Example For x4+2x3–25x2–26x+120: POLYEVAL([1,2,-25,-26,120],8) returns 3432. POLYFORM Polynomial form. Creates a polynomial in variable1 from expression. POLYFORM(expression,variable1) Example POLYFORM((X+1)^2+1,X) returns X^2+2*X+2. POLYROOT Polynomial roots. Returns the roots for the nth-order polynomial with the specified n+1 coefficients. POLYROOT([coefficients]) Example For x4+2x3–25x2–26x+120: POLYROOT([1,2,-25,-26,120]) returns [2,-3,4,-5]. Using mathematical functions HINT The results of POLYROOT will often not be easily seen in HOME due to the number of decimal places, especially if they are complex numbers. It is better to store the results of POLYROOT to a matrix. For example, POLYROOT([1,0,0,-8]672?_M1 will store the three complex cube roots of 8 to matrix M1 as a complex vector. Then you can see them easily by going to the Matrix Catalog. and access them individually in calculations by referring to M1(1), M1(2) etc. Probability functions COMB Number of combinations (without regard to order) of n things taken r at a time: n!/(r!(n- r)). COMB(n,r) Example COMB(5,2) returns 10. That is, there are ten different ways that five things can be combined two at a time. ! Factorial of a positive integer. For non-integers, ! = G (x + 1). This calculates the gamma function. value! PERM Number of permutations (with regard to order) of n things taken r at a time: n!/ (n-r)!. PERM(n,r) Example PERM(5,2) returns 20. That is, there are 20 different permutations of five things taken two at a time. RANDOM Random number (between zero and 1). Produced by a pseudorandom number sequence. The algorithm used in the RANDOM function uses a “seed” number to begin its sequence. To ensure that two calculators must produce different results for the RANDOM function, use the RANDSEED function to seed different starting values before using RANDOM to produce the numbers. RANDOM Using mathematical functions HIN T The setting of Time will be different for each calculator, so using RANDSEED(Time) is guaranteed to produce a set of numbers which are as close to random as possible. You can set the seed using the command RANDSEED. UTPC Upper-Tail Chi-Squared Probability given degrees of freedom, evaluated at value. Returns the probability that a c 2 random variable is greater than value. UTPC(degrees,value) UTPF Upper-Tail Snedecor’s F Probability given numerator degrees of freedom and denominator degrees of freedom (of the F distribution), evaluated at value. Returns the probability that a Snedecor's F random variable is greater than value. UTPF(numerator,denominator,value) UTPN Upper-Tail Normal Probability given mean and variance, evaluated at value. Returns the probability that a normal random variable is greater than value for a normal distribution. Note...

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