Mathematics Branches, Topics, and Sub-Topics

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33Fxx Computational aspects

This subtopic studies computational aspects of special functions, focusing on algorithmic evaluation, symbolic manipulation, and numerical stability.

Specific topics

33F05 Numerical approximation and evaluation of special functions

Overview

33F05 studies numerical approximation and evaluation of special functions in computational aspects of special functions. It studies algorithms and symbolic-numeric methods for evaluating and transforming special functions.

Related Wikipedia Page

Computational Aspects Of Special Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for numerical approximation and evaluation of special functions
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in computer algebra, numerical analysis, and special-function software.

Applications

  • Symbolic computation
  • Stable numerical evaluation
  • Function transformation algorithms

References

Recommended Textbooks

33F10 Symbolic computation of special functions

Overview

33F10 studies symbolic computation of special functions in computational aspects of special functions. It studies algorithms and symbolic-numeric methods for evaluating and transforming special functions.

Related Wikipedia Page

Computational Aspects Of Special Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for symbolic computation of special functions
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in computer algebra, numerical analysis, and special-function software.

Applications

  • Symbolic computation
  • Stable numerical evaluation
  • Function transformation algorithms

References

Recommended Textbooks