Chapter 3: Gamma, Beta, Zeta, and Other Named Functions

The following sections are included:

• Scope of Chapter

• Gamma Function

• The Beta Function

• The Riemann Zeta Function

• The Dirac Delta Function

• Dirichlet Integrals

• Applications

  • Additional Properties of Γ(z)

  • A Definite Integral Containing Logarithms

  • A Class of Important Integrals

  • A Representation for x^−p

  • Additional Properties of the Beta Function

  • Fermi-Dirac Integrals

  • An Integral Involving an Exponential

  • Fermi-Dirac Integrals Containing Logarithms

  • Magnetic Moment of the Electron

  • Relationship Between the Theta and Delta Functions

  • Evaluation of Integrals by Use of the Beta Function

• Other Named Functions

  • Elliptic Integrals of the First and Second Kind

  • Jacobi Elliptic Functions

  • Evaluation of Integrals

  • Comments and References

  • Bibliography