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

Murray R. Spiegel: Mathematical Handbook of Formulas and Tables

Published 1968, Schaum.

ISBN 0-07-060224-7

Part I: Formulas

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 II: Tables

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: $\left({1 + r}\right)^n$

24. Present Value of an Amount: $\left({1 + r}\right)^{-n}$

25. Amount of an Annuity: $\dfrac {\left({1 + r}\right)^n - 1} r$

26. Present Value of an Annuity: $\dfrac {1 - \left({1 + r}\right)^{-n}} r$

27. Bessel functions $J_0 \left({x}\right)$

28. Bessel functions $J_1 \left({x}\right)$

29. Bessel functions $Y_0 \left({x}\right)$

30. Bessel functions $Y_1 \left({x}\right)$

31. Bessel functions $I_0 \left({x}\right)$

32. Bessel functions $I_1 \left({x}\right)$

33. Bessel functions $K_0 \left({x}\right)$

34. Bessel functions $K_1 \left({x}\right)$

35. Bessel functions $\operatorname{Ber} \left({x}\right)$

36. Bessel functions $\operatorname{Bei} \left({x}\right)$

37. Bessel functions $\operatorname{Ker} \left({x}\right)$

38. Bessel functions $\operatorname{Kei} \left({x}\right)$

39. Values for Approximate Zeros of Bessel Functions

40. Exponential, Sine and Cosine Integrals

41. Legendre Polynomials $P_n \left({x}\right)$

42. Legendre Polynomials $P_n \left({\cos \theta}\right)$

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