Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables

Part $\text I$: Formulas

 * The Greek Alphabet
 * 1. Special Constants
 * 2. Special Products and Factors
 * 3. The Binomial Formula and Binomial Coefficients
 * 4. Geometric Formulas
 * 5. Trigonometric Functions
 * 6. Complex Numbers
 * 7. Exponential and Logarithmic Functions
 * 8. Hyperbolic Functions
 * 9. Solutions of Algebraic Equations
 * 10. Formulas from Plane Analytic Geometry
 * 11. Special Plane Curves
 * 12. Formulas from Solid Analytic Geometry
 * 13. Derivatives
 * 14. Indefinite Integrals
 * 15. Definite Integrals
 * 16. The Gamma Function
 * 17. The Beta Function
 * 18. Basic Differential Equations and Solutions
 * 19. Series of Constants
 * 20. Taylor Series
 * 21. Bernoulli and Euler Numbers
 * 22. Formulas from Vector Analysis
 * 23. Fourier Series
 * 24. Bessel Functions
 * 25. Legendre Functions
 * 26. Associated Legendre Functions
 * 27. Hermite Polynomials
 * 28. Laguerre Polynomials
 * 29. Associated Laguerre Polynomials
 * 30. Chebyshev Polynomials
 * 31. Hypergeometric Functions
 * 32. Laplace Transforms
 * 33. Fourier Transforms
 * 34. Elliptic Functions
 * 35. Miscellaneous Special Functions
 * 36. Inequalities
 * 37. Partial Fraction Expansions
 * 38. Infinite Products
 * 39. Probability Distributions
 * 40. Special Moments of Inertia
 * 41. Conversion Factors

Part $\text {II}$: Tables

 * Sample Problems


 * 1. Four Place Common Logarithms
 * 2. Four Place Common Antilogarithms
 * 3. $\operatorname{Sin} x$ ($x$ in degrees and minutes)
 * 4. $\operatorname{Cos} x$ ($x$ in degrees and minutes)
 * 5. $\operatorname{Tan} x$ ($x$ in degrees and minutes)
 * 6. $\operatorname{Cot} x$ ($x$ in degrees and minutes)
 * 7. $\operatorname{Sec} x$ ($x$ in degrees and minutes)
 * 8. $\operatorname{Csc} x$ ($x$ in degrees and minutes)
 * 9. Natural Trigonometric Functions (in radians)
 * 10. $\log \sin x$ ($x$ in degrees and minutes)
 * 11. $\log \cos x$ ($x$ in degrees and minutes)
 * 12. $\log \tan x$ ($x$ in degrees and minutes)
 * 13. Conversion of radians to degrees, minutes and seconds or fractions of a degree
 * 14. Conversion of degrees, minutes and seconds to radians
 * 15. Natural or Napierian Logarithms $\log_e x$ or $\ln x$
 * 16. Exponential functions $e^x$
 * 17. Exponential functions $e^{-x}$
 * 18a. Hyperbolic functions $\sinh x$
 * 18b. Hyperbolic functions $\cosh x$
 * 18c. Hyperbolic functions $\tanh x$
 * 19. Factorial $n$
 * 20. Gamma Function
 * 21. Binomial Coefficients
 * 22. Squares, Cubes, Roots and Reciprocals
 * 23. Compound Amount: $\paren {1 + r}^n$
 * 24. Present Value of an Amount: $\paren {1 + r}^{-n}$
 * 25. Amount of an Annuity: $\dfrac {\paren {1 + r}^n - 1} r$
 * 26. Present Value of an Annuity: $\dfrac {1 - \paren {1 + r}^{-n}} r$
 * 27. Bessel functions $\map {J_0} x$
 * 28. Bessel functions $\map {J_1} x$
 * 29. Bessel functions $\map {Y_0} x$
 * 30. Bessel functions $\map {Y_1} x$
 * 31. Bessel functions $\map {I_0} x$
 * 32. Bessel functions $\map {I_1} x$
 * 33. Bessel functions $\map {K_0} x$
 * 34. Bessel functions $\map {K_1} x$
 * 35. Bessel functions $\map {\operatorname{Ber} } x$
 * 36. Bessel functions $\map {\operatorname{Bei} } x$
 * 37. Bessel functions $\map {\operatorname{Ker} } x$
 * 38. Bessel functions $\map {\operatorname{Kei} } x$
 * 39. Values for Approximate Zeros of Bessel Functions
 * 40. Exponential, Sine and Cosine Integrals
 * 41. Legendre Polynomials $\map {P_n} x$
 * 42. Legendre Polynomials $\map {P_n} {\cos \theta}$
 * 43. Complete Elliptic Integrals of First and Second Kinds
 * 44. Incomplete Elliptic Integrals of the First Kind
 * 45. Incomplete Elliptic Integrals of the Second Kind
 * 46. Ordinates of the Standard Normal Curve
 * 47. Areas under the Standard Normal Curve
 * 48. Percentile Values for Student's $t$ Distribution
 * 49. Percentile Values for the Chi Square Distribution
 * 50. $95$th Percentile Values for the $F$ Distribution
 * 51. $99$th Percentile Values for the $F$ Distribution
 * 52. Random Numbers


 * Index of Special Symbols and Notations


 * Index

Errata
Chapter $2$: Special Products and Factors: $2.22$: Difference of Two Odd Powers:

Chapter $5$: Trigonometric Functions: Relationships between Sides and Angles of a Spherical Triangle: $5.99$: Cosine of Half Angle for Spherical Triangles:

Chapter $14$: Indefinite Integrals: General Rules of Integration: $14.30$: Primitive of $\csch u$:

Chapter $14$: Indefinite Integrals: Integrals involving $a x + b$: $14.73$: Primitive of $\dfrac 1 {\paren {a x + b}^3}$:

Chapter $14$: Indefinite Integrals: Integrals involving $a x + b$: $14.79$: Primitive of $\dfrac 1 {x^3 \paren {a x + b}^3}$:

Chapter $14$: Indefinite Integrals: Integrals involving $\sqrt {a x + b}$ and $\sqrt {p x + q}$: $14.120$: Primitive of $\dfrac 1 {\sqrt {\paren {a x + b} \paren {p x + q} } }$:

Chapter $14$: Indefinite Integrals: General Rules of Integration: $14.210$: Primitive of $\dfrac 1 {\sqrt {x^2 - a^2} }$:

Chapter $14$: Indefinite Integrals: General Rules of Integration: $14.211$: Primitive of $\dfrac {x^2} {\sqrt {x^2 - a^2} }$:

Chapter $14$: Indefinite Integrals: Integrals involving $\sqrt {x^2 - a^2}$: $14.216$: Primitive of $\sqrt {x^2 - a^2}$:

The same mistake applies throughout this section: $14.218$, $14.221$, $14.225$, $14.230$, $14.232$, $14.235$.

Where $\map \ln {x + \sqrt {x^2 - a^2} }$ is given, it should be $\ln \size {x + \sqrt {x^2 - a^2} }$, as $x + \sqrt {x^2 - a^2} < 0$ when $x < -a$.

Chapter $14$: Indefinite Integrals: Integrals involving $\sqrt {a^2 - x^2}$: $14.246$: Primitive of $x^2 \sqrt {a^2 - x^2}$:

Source work progress
* : Lots done, but there are gaps -- working through from beginning as follows:


 * : $\S 4$: Geometric Formulas: $4.24$: Solid geometry $4.25$ to $4.48$ to be done


 * Then by chapters (work in progress):


 * : $\S 10$: Formulas from Plane Analytic Geometry: $10.10$: Area of Triangle with Vertices at $\tuple {x_1, y_1}$, $\tuple {x_2, y_2}$, $\tuple {x_3, y_3}$


 * : $\S 12$: Formulas from Solid Analytic Geometry: Distance $d$ between Two Points $\map {P_1} {x_1, y_1, z_1}$ and $\map {P_2} {x_2, y_2, z_2}$: $12.1$


 * : $\S 39$: Probability Distributions: Poisson Distribution: $39.2$