A Table of Integrals

  title={A Table of Integrals},
  author={Joseph Lipka and Ralph Gorton Hudson},
Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = − 

Topics from this paper

For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x2), arithmetic properties of
The Multiple Zeta Function and the Computation of Some Integrals in Compact Form
Based on the Euler-Zagier multiple zeta function ζ and the extended zeta function ζ, we compute integrals of the form I± k,l,r,m = ∫ 1 0 (− log (1± x)) (1± x) · x r (− log x) dx, J± l,r,m,k = ∫ 1 0
Determining Formulas for the Approximation of the Complete Elliptic Integrals
  • N. Bagis
  • Mathematics
    Current Topics on Mathematics and Computer Science Vol. 8
  • 2021
In this article we give evaluations of the two complete elliptic integrals K and E in the form of Ramanujan’s type-1/π formulas. The result is a formula for Γ(1/4) 2 π −3/2 with accuracy about 120
We give a class of sequences with the argument of the logarithmic term modied and that converge quickly to a generalization of Euler's constant denoted by (a), i.e. the limit of the sequence P n=1 1
The Partition Function of the Dirichlet Operator D 2 s = ∑ d i = 1 ( − ∂ 2 i ) s on a d-Dimensional Rectangle Cavity
In this letter we study the asymptotic behavior of the free partition function in the t → 0 limit for a stochastic process which consists of d−independent, one-dimensional, symmetric, 2s−stable
Periodic solutions of the functional equation f(t)2 + g(t)2 = 1
A general analysis is given of the periodic solutions to the functional equation , where it is assumed that and have continuous second-order derivatives. Under certain conditions we demonstrate that
On the asymptotics of polynomial interpolation to |x|a at the Chebyshev nodes
  • M. Revers
  • Computer Science
    J. Approx. Theory
  • 2013
Asymptotic relations for the approximation of |x |α , α > 0 in L∞ [−1, 1] by Lagrange interpolation polynomials based on the zeros of the Chebyshev polynmials of first kind are discussed.
One Special Identity between the complete elliptic integrals of the first and the third kind
I prove an identity between the first kind and the third kind complete elliptic integrals with the following form: $$\Pi({(1+x) (1-3 x)\over (1-x) (1+3 x)}, {(1+x)^3(1-3 x)\over (1-x)^3 (1+3x)})-
Hybrid bounds for quadratic Weyl sums and arithmetic applications
Let D < 0 be an odd fundamental discriminant and q be a prime number which splits in Q( √ D). Given a suitable smooth function f supported on [X, 2X] for X ≥ 1, we establish a uniform bound in X,D
Angular integrals in d dimensions
We discuss the evaluation of certain d-dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in