10. Mathematical Functions

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• ☰ 1. Introduction to ROOT
  • ☰ 1.1. What Is ROOT?
  • ☰ 1.2. Installing ROOT
  • ☰ 1.3. Starting ROOT
  • ☰ 1.4. Your First ROOT Session
• ☰ 2. C++ Basics for ROOT
  • ☰ 2.1. Why ROOT Uses C++
  • ☰ 2.2. Variables and Data Types
  • ☰ 2.3. Operators
  • ☰ 2.4. Conditional Statements
  • ☰ 2.5. Loops
  • ☰ 2.6. Functions
  • ☰ 2.7. Arrays and Vectors
• ☰ 3. ROOT Macros
  • ☰ 3.1. What Is a ROOT Macro?
  • ☰ 3.2. Running ROOT Macros
  • ☰ 3.3. Functions Inside ROOT Macros
  • ☰ 3.4. Compiling ROOT Macros
  • ☰ 3.5. Organizing a ROOT Project
• ☰ 4. ROOT Objects and the ROOT Object Model
  • ☰ 4.1. Introduction to ROOT Classes
  • ☰ 4.2. Object Names and Titles
  • ☰ 4.3. ROOT Collections
  • ☰ 4.4. Inspecting ROOT Objects
• ☰ 5. Histograms
  • ☰ 5.1. Introduction to Histograms
  • ☰ 5.2. Creating a 1D Histogram
  • ☰ 5.3. Filling Histograms
  • ☰ 5.4. Drawing Histograms
  • ☰ 5.5. Histogram Properties
  • ☰ 5.6. Accessing Histogram Bins
  • ☰ 5.7. Histogram Errors
  • ☰ 5.8. Normalizing Histograms
  • ☰ 5.9. Combining Histograms
• ☰ 6. Two-Dimensional Histograms
  • ☰ 6.1. Creating 2D Histograms
  • ☰ 6.2. Filling 2D Histograms
  • ☰ 6.3. Drawing 2D Histograms
  • ☰ 6.4. Projections
  • ☰ 6.5. Profiles
• ☰ 7. Graphs
  • ☰ 7.1. Introduction to TGraph
  • ☰ 7.2. Creating a TGraph
  • ☰ 7.3. Graph Styling
  • ☰ 7.4. TGraphErrors
  • ☰ 7.5. TGraphAsymmErrors
  • ☰ 7.6. MultiGraph
• ☰ 8. Canvases and Plotting
  • ☰ 8.1. TCanvas
  • ☰ 8.2. Dividing a Canvas
  • ☰ 8.3. Drawing Multiple Objects
  • ☰ 8.4. Legends
  • ☰ 8.5. Text and Annotations
  • ☰ 8.6. Logarithmic Axes
  • ☰ 8.7. Saving Plots
• ☰ 9. Styling ROOT Plots
  • ☰ 9.1. ROOT Plot Styles
  • ☰ 9.2. Axis Configuration
  • ☰ 9.3. Line Styles
  • ☰ 9.4. Marker Styles
  • ☰ 9.5. Publication-Quality Figures
• ☰ 10. Mathematical Functions
  • ☰ 10.1. Introduction to TF1
  • ☰ 10.2. Built-in Functions
  • ☰ 10.3. Custom Functions
  • ☰ 10.4. Evaluating Functions
  • ☰ 10.5. Function Integrals
• ☰ 11. Curve Fitting
  • ☰ 11.1. Introduction to Fitting
  • ☰ 11.2. Gaussian Fits
  • ☰ 11.3. Polynomial Fits
  • ☰ 11.4. Custom Fit Functions
  • ☰ 11.5. Fit Parameters
  • ☰ 11.6. Goodness of Fit
  • ☰ 11.7. Fit Residuals
  • ☰ 11.8. Fitting Graphs
• ☰ 12. ROOT Files
  • ☰ 12.1. Introduction to ROOT Files
  • ☰ 12.2. Creating ROOT Files
  • ☰ 12.3. Writing Objects
  • ☰ 12.4. Reading ROOT Files
  • ☰ 12.5. Exploring ROOT Files
  • ☰ 12.6. Directories Inside ROOT Files
• ☰ 13. TTrees
  • ☰ 13.1. Introduction to TTrees
  • ☰ 13.2. Creating a TTree
  • ☰ 13.3. Filling a TTree
  • ☰ 13.4. Writing a TTree to a File
  • ☰ 13.5. Reading a TTree
  • ☰ 13.6. Inspecting TTrees
  • ☰ 13.7. Drawing Data from TTrees
  • ☰ 13.8. Applying Selection Cuts
  • ☰ 13.9. Branch Addresses
• ☰ 14. Event-Based Data Analysis
  • ☰ 14.1. Understanding Event Data
  • ☰ 14.2. Event Loops
  • ☰ 14.3. Event Selection
  • ☰ 14.4. Derived Quantities
  • ☰ 14.5. Analysis Workflow
• ☰ 15. Working with Real Experimental Data
  • ☰ 15.1. Importing Text Data
  • ☰ 15.2. Converting Data to ROOT
  • ☰ 15.3. Data Cleaning
  • ☰ 15.4. Data Calibration
  • ☰ 15.5. Signal and Background
• ☰ 16. Random Numbers and Simulations
  • ☰ 16.1. Random Number Generation
  • ☰ 16.2. Common Distributions
  • ☰ 16.3. Simple Monte Carlo Simulation
  • ☰ 16.4. Detector Resolution Simulation
  • ☰ 16.5. Efficiency Simulation
• ☰ 17. Statistical Analysis with ROOT
  • ☰ 17.1. Basic Statistics
  • ☰ 17.2. Probability Distributions
  • ☰ 17.3. Statistical Uncertainties
  • ☰ 17.4. Chi-Square Tests
  • ☰ 17.5. Confidence Intervals
• ☰ 18. Modern ROOT with RDataFrame
  • ☰ 18.1. Introduction to RDataFrame
  • ☰ 18.2. Loading Data
  • ☰ 18.3. Filtering Data
  • ☰ 18.4. Defining New Columns
  • ☰ 18.5. Creating Histograms
  • ☰ 18.6. Statistical Operations
  • ☰ 18.7. Saving Results
  • ☰ 18.8. Multithreading
• ☰ 19. ROOT and Python
  • ☰ 19.1. Introduction to PyROOT
  • ☰ 19.2. ROOT Objects in Python
  • ☰ 19.3. Reading ROOT Files with Python
  • ☰ 19.4. PyROOT and NumPy
  • ☰ 19.5. PyROOT and Matplotlib
  • ☰ 19.6. Choosing Between C++ and Python
• ☰ 20. Advanced TTree Techniques
  • ☰ 20.1. Trees with Multiple Branches
  • ☰ 20.2. Storing std::vector Objects
  • ☰ 20.3. TChain
  • ☰ 20.4. Friends
  • ☰ 20.5. Efficient TTree Analysis
• ☰ 21. ROOT for Particle and Nuclear Physics
  • ☰ 21.1. Four-Vectors
  • ☰ 21.2. Particle Kinematics
  • ☰ 21.3. Invariant Mass
  • ☰ 21.4. Angular Distributions
  • ☰ 21.5. Detector Spectra
• ☰ 22. Debugging and Common ROOT Problems
  • ☰ 22.1. ROOT Object Ownership
  • ☰ 22.2. Null Pointers
  • ☰ 22.3. Segmentation Faults
  • ☰ 22.4. Missing Histograms
  • ☰ 22.5. ROOT File Problems
  • ☰ 22.6. TTree Branch Problems
  • ☰ 22.7. Histogram Range Problems
  • ☰ 22.8. Fit Failures
  • ☰ 22.9. Debugging ROOT Macros
• ☰ 23. Writing Better ROOT Analysis Code
  • ☰ 23.1. Separating Analysis and Plotting
  • ☰ 23.2. Using Functions
  • ☰ 23.3. Using Header Files
  • ☰ 23.4. Naming Conventions
  • ☰ 23.5. Avoiding Hard-Coded Values
  • ☰ 23.6. Configuration Parameters
  • ☰ 23.7. Reproducible Analysis
  • ☰ 23.8. Version Control with Git
• ☰ 24. Final Project
  • ☰ 24.1. Project Overview
  • ☰ 24.2. Analyze a complete scientific dataset using ROOT.
  • ☰ 24.3. Import the Data
  • ☰ 24.4. Explore the Dataset
  • ☰ 24.5. Apply Data Selection
  • ☰ 24.6. Create Histograms
  • ☰ 24.7. Fit the Data
  • ☰ 24.8. Calculate Physical Quantities
  • ☰ 24.9. Estimate Statistical Uncertainties
  • ☰ 24.10. Create Publication-Quality Figures
  • ☰ 24.11. Save the Analysis Results
  • ☰ 24.12. Write a Short Analysis Report
• ☰ 25. Appendices
  • ☰ 25.1. A. ROOT Command Cheat Sheet
  • ☰ 25.2. B. ROOT Histogram Classes
  • ☰ 25.3. C. ROOT Graph Classes
  • ☰ 25.4. D. Common TTree Commands
  • ☰ 25.5. E. Common Drawing Options
  • ☰ 25.6. F. Common Fit Functions
  • ☰ 25.7. G. ROOT C++ Cheat Sheet
  • ☰ 25.8. H. PyROOT Cheat Sheet
  • ☰ 25.9. I. Common ROOT Errors and Solutions
  • ☰ 25.10. J. Recommended ROOT Analysis Workflow