An Atlas of Functions

2. General Considerations
Keith B. Oldham, Jan C. Myland, Jerome Spanier

3. The Constant Function c

Keith B. Oldham, Jan C. Myland, Jerome Spanier

4. The Factorial Function n!
Keith B. Oldham, Jan C. Myland, Jerome Spanier

5. The Zeta Numbers and Related Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

6. The Bernoulli Numbers B
n


Keith B. Oldham, Jan C. Myland, Jerome Spanier

7. The Euler Numbers E
n


Keith B. Oldham, Jan C. Myland, Jerome Spanier

8. The Binomial Coefficients _m^v
Keith B. Oldham, Jan C. Myland, Jerome Spanier

9. The Linear Function bx + c and Its Reciprocal
Keith B. Oldham, Jan C. Myland, Jerome Spanier

10. Modifying Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

11. The Heaviside u(x−a) And Dirac δ(x−a) Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

12. The Integer Powers x

n
And (bx+c)
n


Keith B. Oldham, Jan C. Myland, Jerome Spanier

13. The Square-Root Function sqrt (bx + c) and Its Reciprocal
Keith B. Oldham, Jan C. Myland, Jerome Spanier

14. The Noninteger Powers x

v


Keith B. Oldham, Jan C. Myland, Jerome Spanier

15. The Semielliptic Function b/a sqrt (a^2 - x^2) and Its Reciprocal
Keith B. Oldham, Jan C. Myland, Jerome Spanier

16. The Semihyperbolic Functions b/a sqrt (x^2 a^2) And Their Reciprocals
Keith B. Oldham, Jan C. Myland, Jerome Spanier

17. The Quadratic Function ax
2+bx+c and Its Reciprocal
Keith B. Oldham, Jan C. Myland, Jerome Spanier

18. The Cubic Function x
3 + ax
2 + bx + c

Keith B. Oldham, Jan C. Myland, Jerome Spanier

19. Polynomial Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

20. The Pochhammer Polynomials (x)
n


Keith B. Oldham, Jan C. Myland, Jerome Spanier

21. The Bernoulli Polynomials B
n
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

22. The Euler Polynomials E
n
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

23. The Legendre Polynomials P
n
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

24. The Chebyshev Polynomials T
n
(x) and U
n
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

25. The Laguerre Polynomials L
n
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

26. The Hermite Polynomials H
n
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

27. The Logarithmic Function ln(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

28. The Exponential Function exp(±x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

29. Exponentials of Powers exp(± x

v
)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

30. The Hyperbolic Cosine Cosh(x) and Sine Sinh(x) Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

31. The Hyperbolic Secant Sech(x) and Cosecant Csch(x) Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

32. The Hyperbolic Tangent tanh(x) and Cotangent coth(x) Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

33. The Inverse Hyperbolic Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

34. The Cosine cos(x) and Sine sin(x) Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

35. The Secant sec(x) And cosecant csc(x) Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

36. The Tangent tan(x) and Cotangent cot(x) Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

37. The Inverse Circular Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

38. Periodic Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

39. The Exponential Integrals Ei(x) and Ein(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

40. Sine and Cosine Integrals
Keith B. Oldham, Jan C. Myland, Jerome Spanier

41. The Fresnel Integrals C(x) and S(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

42. The Error Function erf(x) and Its Complement erfc(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

43. The exp(x) erfc sqrt x and Related Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

44. Dawson’s Integral daw(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

45. The Gamma Function Γ(v)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

46. The Digamma Function ψ(v)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

47. The Incomplete Gamma Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

48. The Parabolic Cylinder Function D
v
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

49. The Kummer Function M(a,c,x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

50. The Tricomi Function U(a,c,x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

51. The Modified Bessel Functions I
n
(x) of Integer Order
Keith B. Oldham, Jan C. Myland, Jerome Spanier

52. The Modified Bessel Function I
v
(x) of Arbitrary Order
Keith B. Oldham, Jan C. Myland, Jerome Spanier

53. The Macdonald Function K
v
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

54. The Bessel Functions J
n
(x) of Integer Order
Keith B. Oldham, Jan C. Myland, Jerome Spanier

55. The Bessel Function J
v
(x) of Arbitrary Order
Keith B. Oldham, Jan C. Myland, Jerome Spanier

56. The Neumann Function Y
v
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

57. The Kelvin Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

58. The Airy Functions Ai(x) and Bi(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

59. The Struve Function h
v
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

60. The Incomplete Beta Function B(v,μ,x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

61. The Legendre Functions P
v
(x) and Q
v
(x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

62. The Gauss Hypergeometric Function F(a,b,c,x)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

63. The Complete Elliptic Integrals K(k) and E(k)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

64. The Incomplete Elliptic Integrals F(k,ϕ) AND E(k,ϕ)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

65. The Jacobian Elliptic Functions
Keith B. Oldham, Jan C. Myland, Jerome Spanier

66. The Hurwitz Function ζ(v, u)
Keith B. Oldham, Jan C. Myland, Jerome Spanier

Keywords: Mathematics, Applications of Mathematics, Special Functions, Real Functions, Mathematical and Computational Physics, Computational Intelligence