| \(\exp(a)\) | Natural Exponential Function | \(e^a\) |
| \(\ln(a)\) | Natural Logarithm | \(\log_e(a))\) |
| \(\log(a)\) | Common Logarithm | \(\log_{10}(a)\) |
| \(\log_b(a)\) | Logarithm | \(\frac{\int_1^a\frac1t\text{dt}}{\int_1^b\frac1t\text{dt}}\) |
| \(\operatorname{total}(L)\) | Sum of all values in list | \(\sum L\) |
| \(\operatorname{count}(L)\) | Number of elements in list | \(L=[L_1,\ldots,L_n];n\) |
| \(\operatorname{mean}(L)\) | Arithmetic Mean | \(\frac{1}{n}\sum_{k=1}^nL_k\) |
| \(\operatorname{mean}(x_1,\ldots,x_n)\) | Arithmetic Mean | \(\frac{1}{n}\sum_{k=1}^nx_k\) |
| \(\operatorname{median}(L)\) | Statistical Median | \(\begin{cases}(L.\kern-.15em\operatorname{sort})_\frac{n+1}{2} & n\text{ is odd}\\\frac{1}{2}\big((L.\kern-.15em\operatorname{sort})_\frac{n}{2}+(L.\kern-.15em\operatorname{sort})_\frac{n+1}{2}\big) & n\text{ is even}\end{cases}\) |
| \(\operatorname{median}(x_1,\ldots,x_n)\) | Statistical Median | \(L=[x_1,\ldots,x_n];\\\begin{cases}(L.\kern-.15em\operatorname{sort})_\frac{n+1}{2} & n\text{ is odd}\\\frac{1}{2}\big((L.\kern-.15em\operatorname{sort})_\frac{n}{2}+(L.\kern-.15em\operatorname{sort})_\frac{n+1}{2}\big) & n\text{ is even}\end{cases}\) |
| \(\operatorname{quartile}(L, q)\) | Moore and McCabe Quartile | \(\begin{cases}\frac{n+1}{4} & n\text{ is odd and }q=1\\\frac{3n+3}{4} & n\text{ is odd and }q=3\\\frac{n+2}{4} & n\text{ is even and }q=1\\\frac{3n+2}{4} & n\text{ is even and }q=3\\\end{cases}\) |
| \(\operatorname{nCr}(n,r)\) | Binomial Coefficient | \(\prod_{i=1}^r\frac{n+1-i}{i}\) |
| \(\operatorname{nPr}(n,r)\) | r-permutation of n | \(\frac{n!}{(n-k)!}\) |
| \(\operatorname{stdev}(L)\) | Standard Deviation | \(\sqrt{\frac1{n-1}\sum_{i=1}^n(L_i-L.\kern-.15em\operatorname{mean})^2}\) |
| \(\operatorname{stdev}(x_1,\ldots,x_n)\) | Standard Deviation | \(\sqrt{\frac1{n-1}\sum_{i=1}^n(x_i-\operatorname{mean}(x_1,\ldots,x_n))^2}\) |
| \(\operatorname{stdevp}(L)\) | Population Standard Deviation | \(\sqrt{\frac1n\sum_{i=1}^n(L_i-L.\kern-.15em\operatorname{mean})^2}\) |
| \(\operatorname{stdevp}(x_1,\ldots,x_n)\) | Population Standard Deviation | \(\sqrt{\frac1n\sum_{i=1}^n(x_i-\operatorname{mean}(x_1,\ldots,x_n))^2}\) |
| \(\operatorname{mad}(L)\) | Mean Absolute Deviation | \(\frac1n\sum_{i=1}^n\left|L_i-L.\kern-.15em\operatorname{mean}\right|\) |
| \(\operatorname{mad}(x_1,\ldots,x_n)\) | Mean Absolute Deviation | \(\frac1n\sum_{i=1}^n\left|x_i-\operatorname{mean}(x_1,\ldots,x_n)\right|\) |
| \(\operatorname{var}(L)\) | Variance | \(\frac1{n-1}\sum_{i=1}^n(L_i-L.\kern-.15em\operatorname{mean})^2\) |
| \(\operatorname{var}(x_1,\ldots,x_n)\) | Variance | \(\frac1{n-1}\sum_{i=1}^n(x_i-\operatorname{mean}(x_1,\ldots,x_n))^2\) |
| \(\operatorname{varp}(L)\) | Population Variance | \(\frac1n\sum_{i=1}^n(L_i-L.\kern-.15em\operatorname{mean})^2\) |
| \(\operatorname{varp}(x_1,\ldots,x_n)\) | Population Variance | \(\frac1n\sum_{i=1}^n(x_i-\operatorname{mean}(x_1,\ldots,x_n))^2\) |
| \(\operatorname{cov}(A,B)\) | Covariance | \(\sum_{i=1}^n\frac{(A_i-A.\operatorname{mean})(B_i-B.\operatorname{mean})}{N-1}\) |
| \(\operatorname{covp}(A,B)\) | Population Covariance | \(\sum_{i=1}^n\frac{(A_i-A.\operatorname{mean})(B_i-B.\operatorname{mean})}N\) |
| \(\operatorname{corr}(A,B)\) | Pearson Correlation Coefficient | \(\frac{\operatorname{cov}(A,B)}{\operatorname{stdev}(A)\operatorname{stdev}(B)}\) |
| \(\operatorname{spearman}(A,B)\) | Spearman's Rank Correlation Coefficient | \(C=[1,\ldots,A.\kern-.15em\operatorname{count}].\kern-.15em\operatorname{sort}(A)\\D=[1,\ldots,B.\kern-.15em\operatorname{count}].\kern-.15em\operatorname{sort}(B)\\\operatorname{corr}(C,D)\) |
| \(\operatorname{lcm}(L)\) | | |
| \(\operatorname{lcm}(x_1,\ldots,x_n)\) | | |
| \(\operatorname{gcd}(L)\) | | |
| \(\operatorname{gcd}(x_1,\ldots,x_n)\) | | |
| \(\operatorname{mod}(a,n)\) | Remainder of Integer Division | \(a-n\left\lfloor\frac an\right\rfloor\) |
| \(\operatorname{floor}(a)\) | Round down | |
| \(\operatorname{ceil}(a)\) | Round up | |
| \(\operatorname{round}(a)\) | Round | |
| \(\operatorname{round}(a,b)\) | Round to \(b\) decimal places | |
| \(\operatorname{abs}(a)\) | Absolute Value | \(\begin{cases}a&a\ge0\\-a&a\lt0\end{cases}\) |
| \(\operatorname{min}(L)\) | Least element of \(L\) | |
| \(\operatorname{min}(x_1,\ldots,x_n)\) | Least of \(x_1,\ldots,x_n\) | |
| \(\operatorname{max}(L)\) | Greatest element of \(L\) | |
| \(\operatorname{max}(x_1,\ldots,x_n)\) | Greatest of \(x_1,\ldots,x_n\) | |
| \(\operatorname{sign}(a)\) | Signum | \(\begin{cases}-1&a<0\\0&a=0\\1&a>0\end{cases}\) |
| \(\sin(a)\) | Trigonometric Sine | \(\sum_{n=1}^\infty\frac{(-1)^{n-1}}{(2n-1)!}a^{2n-1}\) |
| \(\cos(a)\) | Trigonometric Cosine | \(\sum_{n=1}^\infty\frac{(-1)^{n}}{(2n)!}a^{2n}\) |
| \(\tan(a)\) | Trigonometric Tangent | \(\frac{\sin a}{\cos a}\) |
| \(\csc(a)\) | Trigonometric Cosecant | \(\frac1{\sin a}\) |
| \(\sec(a)\) | Trigonometric Secant | \(\frac1{\cos a}\) |
| \(\cot(a)\) | Trigonometric Cotangent | \(\frac1{\tan a}\) |
| \(\sinh(a)\) | Hyperbolic Sine | \(\frac12(e^a-e^{-a})\) |
| \(\cosh(a)\) | Hyperbolic Cosine | \(\frac12(e^a+e^{-a})\) |
| \(\tanh(a)\) | Hyperbolic Tangent | \(\frac{\sinh a}{\cosh a}\) |
| \(\operatorname{csch}(a)\) | Hyperbolic Cosecant | \(\frac1{\sinh a}\) |
| \(\operatorname{sech}(a)\) | Hyperbolic Secant | \(\frac1{\cosh a}\) |
| \(\coth(a)\) | Hyperbolic Cotangent | \(\frac{\cosh a}{\sinh a}\) |
| \(\arcsin(a)\) | | |
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