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Handbook of Mathematical Formulas and Integrals

Quick Reference List of Frequently Used Data:Useful Identities
Numerical, Algebraic, and Analytical Results for Series and Calculus:Finite Sums, Determinants
Functions and Identities:Logorithms and Exponentials, Trigonometric Identities
Derivatives of Elementary Functions:Derivatives of Inverse Hyperbolic Functions
Indefinite Integrals of Algebraic Functions:Algebraic and Transcendental Functions
Indefinite Integrals of Exponential Functions:Basic Results, Indefinite Integrals Involving eax
Indefinite Integrals of Logarithmic Functions:Combinations of Logarithms and Polynomials, The Logarithm
Indefinite Integrals of Hyperbolic Functions:Basic Results, Integrands Involving tanh kx and coth kx
Indefinite Integrals Involving Inverse Hyperbolic Functions:Basic Results
Indefinite Integrals of Trigonometric Functions:Integrands Involving tan x and/or cot x
Indefinite Integrals of Inverse Trigonometric Functions:Integrands Involving xn arcsinm(x/a)
The Gamma, Beta, Pi, and Psi Functions, and the Incomplete Gamma Functions:Definitions and Notation
Elliptic Integrals and Functions:Elliptic Integrals, Legendre Normal Forms, Jacobian Elliptic Functions
Probability Distributions and Integrals, and the Error Function:Distributions, The Error Function
Fresnel Integrals, Sine and Cosine Integrals:The Fresnel Integrals, Sine and Cosine Integrals
Definite Integrals:Integrands Involving Trigonometric Functions
Different Forms of Fourier Series:Fourier Series and Discontinuous Functions
Bessel Functions:Besselís Differential Equation, Zeros of Bessel Functions
Orthogonal Polynomials:Legendre Polynomials Pn(x), Hermite Polynomials Hn(x)
Laplace Transformation:Definition of the Laplace Transform, Laplace Transform Pairs
Fourier Transforms:Fourier Exponential Transform, Fourier Cosine and Sine Transform Pairs
Numerical Integration:Classical Methods, Open- and Closed-Type Formulas
Solutions of Standard Ordinary Differential Equations:Basic Definitions, Exact Equations
Vector Analysis:Scalars and Vectors, Triple Products, Products of Four Vectors
Systems of Orthogonal Coordinates:Curvilinear Coordinates, Systems of Orthogonal Coordinates
Partial Differential Equations and Special Functions:Fundamental Ideas, The Method of Characteristics
Qualitative Properties of the Heat and Laplace Equation
Solutions of Elliptic, Parabolic, and Hyperbolic Equations:Hyperbolic Equations
The z-Transform:The z-Transform and Transform Pairs
Numerical Approximation:Linear Interpolation, Lagrange Polynomial Interpolation
Conformal Mapping and Boundary Value Problems:Boundary Value Problems
Short Classified Reference List:General Tables of Integrals, General Reading

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