An Atlas of Functions

General Considerations.- The Constant Function c.- The Factorial Function n!.- The Zeta Numbers and Related Functions.- The Bernoulli Numbers B n .- The Euler Numbers E n .- The Binomial Coefficients .- The Linear Function bx + c and Its Reciprocal.- Modifying Functions.- The Heaviside u(x?a) And Dirac ?(x?a) Functions.- The Integer Powers x n And (bx+c) n .- The Square-Root Function and Its Reciprocal.- The Noninteger Powers x v .- The Semielliptic Function and Its Reciprocal.- The Semihyperbolic Functions And Their Reciprocals.- The Quadratic Function ax 2+bx+c and Its Reciprocal.- The Cubic Function x 3 + ax 2 + bx + c.- Polynomial Functions.- The Pochhammer Polynomials (x) n .- The Bernoulli Polynomials B n (x).- The Euler Polynomials E n (x).- The Legendre Polynomials P n (x).- The Chebyshev Polynomials T n (x) and U n (x).- The Laguerre Polynomials L n (x).- The Hermite Polynomials H n (x).- The Logarithmic Function ln(x).- The Exponential Function exp(±x).- Exponentials of Powers exp(± x v ).- The Hyperbolic Cosine Cosh(x) and Sine Sinh(x) Functions.- The Hyperbolic Secant Sech(x) and Cosecant Csch(x) Functions.- The Hyperbolic Tangent tanh(x) and Cotangent coth(x) Functions.- The Inverse Hyperbolic Functions.- The Cosine cos(x) and Sine sin(x) Functions.- The Secant sec(x) And cosecant csc(x) Functions.- 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 and Related Functions.- Dawson’s Integral daw(x).- The Gamma Function ?(v).- The Digamma Function ?(v).- The Incomplete Gamma Functions.- The Parabolic Cylinder Function D v (x).- The Kummer Function M(a,c,x).- The Tricomi Function U(a,c,x).- The Modified Bessel Functions I n (x) of Integer Order.- The Modified Bessel Function I v (x) of Arbitrary Order.- The Macdonald Function K v (x).- The Bessel Functions J n (x) of Integer Order.- The Bessel Function J v (x) of Arbitrary Order.- The Neumann Function Y v (x).- The Kelvin Functions.- The Airy Functions Ai(x) and Bi(x).- The Struve Function h v (x).- The Incomplete Beta Function B(v,?,x).- The Legendre Functions P v (x) and Q v (x).- The Gauss Hypergeometric Function F(a,b,c,x).- The Complete Elliptic Integrals K(k) and E(k).- The Incomplete Elliptic Integrals F(k,?) AND E(k,?).- The Jacobian Elliptic Functions.- The Hurwitz Function ?(v, u).