Mathematics Branches, Topics, and Sub-Topics

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33Bxx Elementary special functions

This subtopic studies elementary special functions, including classical families that serve as building blocks for more advanced special-function theory.

Specific topics

33B10 Exponential and trigonometric functions

Overview

33B10 studies exponential and trigonometric functions in elementary special functions. It studies foundational special functions such as gamma, beta, and elementary transcendental functions and their identities.

Related Wikipedia Page

Elementary Special Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for exponential and trigonometric 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 approximation, asymptotics, and classical analytic formulas.

Applications

  • Gamma and beta functions
  • Classical transcendental identities
  • Asymptotic analysis

References

Recommended Textbooks

33B15 Gamma, beta and polygamma functions

Overview

33B15 studies gamma, beta and polygamma functions in elementary special functions. It studies foundational special functions such as gamma, beta, and elementary transcendental functions and their identities.

Related Wikipedia Page

Elementary Special Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for gamma, beta and polygamma 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 approximation, asymptotics, and classical analytic formulas.

Applications

  • Gamma and beta functions
  • Classical transcendental identities
  • Asymptotic analysis

References

Recommended Textbooks

33B20 Incomplete beta and gamma functions

Overview

33B20 studies incomplete beta and gamma functions in elementary special functions. It studies foundational special functions such as gamma, beta, and elementary transcendental functions and their identities.

Related Wikipedia Page

Elementary Special Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for incomplete beta and gamma 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 approximation, asymptotics, and classical analytic formulas.

Applications

  • Gamma and beta functions
  • Classical transcendental identities
  • Asymptotic analysis

References

Recommended Textbooks

33B30 Higher logarithm functions

Overview

33B30 studies higher logarithm functions in elementary special functions. It studies foundational special functions such as gamma, beta, and elementary transcendental functions and their identities.

Related Wikipedia Page

Elementary Special Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for higher logarithm 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 approximation, asymptotics, and classical analytic formulas.

Applications

  • Gamma and beta functions
  • Classical transcendental identities
  • Asymptotic analysis

References

Recommended Textbooks

33B99 None of the above

Overview

33B99 studies none of the above in elementary special functions. It studies foundational special functions such as gamma, beta, and elementary transcendental functions and their identities.

Related Wikipedia Page

Elementary Special Functions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for none of the above
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in approximation, asymptotics, and classical analytic formulas.

Applications

  • Gamma and beta functions
  • Classical transcendental identities
  • Asymptotic analysis

References

Recommended Textbooks