05. Evaluation of Functions

5.0 Introduction          . . 201
5.1 Polynomials and Rational Functions      . . 201
5.2 Evaluation of Continued Fractions       206
5.3 Series and Their Convergence       . . 209
5.4 Recurrence Relations and Clenshaw’s Recurrence Formula  . . 219
  5.5 Complex Arithmetic         . 225
  5.6 Quadratic and Cubic Equations       . 227
  5.7 Numerical Derivatives         229
  5.8 Chebyshev Approximation        . 233
  5.9 Derivatives or Integrals of a Chebyshev-Approximated Function . . 240
  5.10 Polynomial Approximation from Chebyshev Coefficients  . . 241
    5.11 Economization of Power Series       . 243
    5.12 Pad ́ Approximants         . 245
     e . . 247
     5.13 Rational Chebyshev Approximation      251
     5.14 Evaluation of Functions by Path Integration    . . 

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Last modification on: Wed, 15 Jul 2026 .