Bernoulli polynomials

Abstract: On operations Functions important in the calculus of finite differences Inverse operation of differences and means. Sums Stirling's numbers Bernoulli polynomials and numbers Euler's and Boole's polynomials. Sums of reciprocal powers Expansion of functions, interpolation, construction of tables Approximation and graduation Numerical solution of equations. Numerical integration Functions of several independent variables Difference equations Partial difference equations.

Abstract: 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.