Macro Reference
Formula Library Reference
Overview
The Formula Library is a curated collection of ready-to-use LaTeX formulas organized into 11 subject categories. Use it as a quick reference when writing technical documentation - copy any formula into the LaTeX Block or LaTeX Inline macro and customize as needed.
How to Use This Library
- Find the formula category that matches your domain
- Copy the LaTeX source code shown
- Open a LaTeX Block macro on your Confluence page
- Paste the formula into the Source panel
- The Preview panel renders it immediately - adjust as needed and Save
Category 1: Algebra & Arithmetic
Quadratic Formula
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Binomial Theorem
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
Geometric Series (Finite)
S_n = a \cdot \frac{1 - r^n}{1 - r}
Category 2: Calculus
Definite Integral
\int_a^b f(x) \, dx = F(b) - F(a)
Chain Rule (Derivative)
\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)
Taylor Series Expansion
f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n
Fundamental Theorem of Calculus
\frac{d}{dx} \int_a^x f(t) \, dt = f(x)
Category 3: Linear Algebra
Matrix Multiplication
(AB)_{ij} = \sum_{k=1}^{n} A_{ik} B_{kj}
Determinant (2×2)
\det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc
Identity Matrix (3×3)
I = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}
Eigenvalue Equation
A\mathbf{v} = \lambda \mathbf{v}
Category 4: Statistics & Probability
Mean (Arithmetic Average)
\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i
Standard Deviation
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}
Normal Distribution PDF
f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}
Bayes' Theorem
P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}
Category 5: Machine Learning & Data Science
Mean Squared Error (MSE)
\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
Cross-Entropy Loss
L = -\sum_{i} y_i \log(\hat{y}_i)
Softmax Function
\sigma(z)_j = \frac{e^{z_j}}{\sum_{k=1}^{K} e^{z_k}}
Sigmoid Function
\sigma(x) = \frac{1}{1 + e^{-x}}
Accuracy
\text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN}
Category 6: Physics & Engineering
Newton's Second Law
F = ma
Kinetic Energy
E_k = \frac{1}{2} m v^2
Einstein's Energy-Mass Equivalence
E = mc^2
Ohm's Law
V = IR
Wave Equation
v = f \lambda
Category 7: SLA & Operations Metrics
Availability (SLA)
\text{Availability} = \frac{\text{MTBF}}{\text{MTBF} + \text{MTTR}} \times 100\%
Mean Time Between Failures (MTBF)
\text{MTBF} = \frac{\text{Total Uptime}}{\text{Number of Failures}}
Mean Time to Recovery (MTTR)
\text{MTTR} = \frac{\text{Total Downtime}}{\text{Number of Incidents}}
Error Rate
\text{Error Rate} = \frac{\text{Failed Requests}}{\text{Total Requests}} \times 100
Category 8: Financial Mathematics
Compound Interest
A = P\left(1 + \frac{r}{n}\right)^{nt}
Net Present Value (NPV)
\text{NPV} = \sum_{t=0}^{T} \frac{C_t}{(1+r)^t}
Return on Investment (ROI)
\text{ROI} = \frac{\text{Net Profit}}{\text{Cost of Investment}} \times 100
Category 9: Information Theory
Shannon Entropy
H(X) = -\sum_{i} p(x_i) \log_2 p(x_i)
Kullback-Leibler Divergence
D_{KL}(P \| Q) = \sum_{x} P(x) \log \frac{P(x)}{Q(x)}
Category 10: Greek Letters & Symbols Reference
| Symbol | LaTeX | Symbol | LaTeX |
|---|---|---|---|
| α (alpha) | \alpha | Σ (Sigma) | \Sigma |
| β (beta) | \beta | π (pi) | \pi |
| γ (gamma) | \gamma | θ (theta) | \theta |
| δ (delta) | \delta | λ (lambda) | \lambda |
| μ (mu) | \mu | ∞ (infinity) | \infty |
| σ (sigma) | \sigma | ± (plus-minus) | \pm |
Category 11: Aligned Derivations & Multi-Line Formulas
Aligned Equations (use aligned environment)
\begin{aligned}
f(x) &= x^2 + 2x + 1 \\
&= (x + 1)^2
\end{aligned}
Cases (Piecewise Functions)
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x & \text{if } x < 0
\end{cases}
System of Equations
\begin{cases}
2x + 3y = 12 \\
x - y = 1
\end{cases}