An Atlas of Functions

Preface.- The Constant Function c.- The Factorial Function n!.- The Zeta Numbers and Related Functions.- The Bernoulli Numbers Bn.- The Euler Numbers En.- The Bionmial Coefficients.- The Linear Function bx + c and Its Reciprocal.- Modifying Functions.- The Heaviside and Dirac Functions.- The Integer Powers xn and (bx + c)n.- The Square-Root Function and Its Reciprocal.- The Noninteger Power xv.- The Semielliptic Function and Its Reciprocal.- The (b/a)square root of x2 +- a2 Functions and Their Reciprocals.- The Quadratic Function ax + bx + c and Its Reciprocal.- The Cubic Function x3 + bx + c.- Polynomial Functions.- The Pochhammer Polynomials (x)n.- The Bernoulli Polynomials Bn(x).- The Euler Polynomials En(x).- The Legendre Polynomials Pn(x).- The Chebyshev Polynomials Tn(x) and Un(x).- The Laguerre Polynomials Ln(x).- The Hermite Polynomials Hn(x).- The Logarithmic Function ln(x).- The Exponential Function exp(x).- Exponential of Powers.- The Hyperbolic Cosine cosh(x). and Sine sinh(x) Functions.- The Hyperbolic Secant and Cosecant Functions.- The Inverse Hyperbolic Functions.- The Cosine cox(x) and Sine sin(x) Functions.- The Secant sec(x) and Cosecant csc(x) Fucntions.- The Tangent tan(x) and Cotangent cot(x) Functions.- The Inverse Circular Functions.- Periodic Functions.- The Exponential Integrals Ei(x) and Ein(x).- Sine and Cosine Integrals.- The Fresnel Integrals C(x) and S(x).- The Error Function erf(x) and Its Complement erfc(x).- The exp(x)erfc(square root of x) and Related Functions.- Dawson's Integral daw(x).- The Gamma Function.- The Digamma Function.- The Incomplete Gamma Functions.- The Parabolic Cylinder Function Dv(x).- The Kummer Function M(a, c, x).- The Tricomi Function U(a, c, x).- The Modified Bessel Functions In(x) of Integer Order.- The Modified Bessel Functions of In(x) Arbitrary Order.- The Macdonald Function Kv(x).- The Bessel Functions Jn(x) of Integer Order.- The Bessel Functions Jv(x) of Arbitrary Order.- The Neumann Function Yv(x). The Kelvin Functions.- The Airy Functions Ai(x) and Bi(x).- The Struve Function hv(x).- The Incomplete Beta Function.- The Legendre Functions Pv(x) and Qv(x).- The Gauss Hypergeometric Function F(a,b,c,x).- The Complete Elliptic Integrals K(k) and E(k).- The Incomplete Elliptic Integrals.- The Jacobian Elliptic Functions.- The Hurwitz Function.- Appendix A: Useful Data.- Appendix B: Bibliography.- Appendix C: Equator, The Atlas Function Calculator.- Symbol Index.- Subject Index.