Verifying DLMF with Maple and Mathematica
This page presents the results of the publication Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems.
Bug Reports
You can find a PDF with commands that illustrate the encountered errors in Mathematica here: File:Mathematica Bugs Overview.pdf
We provide the same file as the Wolfram system notebook format (NB) here: File:Mathematica Bugs Notebook File.nb
DLMF Translations and Results
In the following, we present the translations of the DLMF equations to the CAS Maple and Mathematica.
DLMF | Formula | Translations Maple |
Translations Mathematica |
Symbolic Evaluation Maple |
Symbolic Evaluation Mathematica |
Numeric Evaluation Maple |
Numeric Evaluation Mathematica |
---|---|---|---|---|---|---|---|
DLMF | 6,623 | 4,114 (62.1%) | 4,713 (71.2%) | 1,084 (26.3%) | 1,235 (26.2%) | 698 (26.7%) | 784 (22.6%) |
Results of the Digital Library of Mathematical Functions
- Algebraic and Analytic Methods
- Asymptotic Approximations
- Numerical Methods
- Elementary Functions
- Gamma Function
- Exponential, Logarithmic, Sine, and Cosine Integrals
- Error Functions, Dawson’s and Fresnel Integrals
- Incomplete Gamma and Related Functions
- Airy and Related Functions
- Bessel Functions
- Struve and Related Functions
- Parabolic Cylinder Functions
- Confluent Hypergeometric Functions
- Legendre and Related Functions
- Hypergeometric Function
- Generalized Hypergeometric Functions and Meijer G-Function
- q-Hypergeometric and Related Functions
- Orthogonal Polynomials
- Elliptic Integrals
- Theta Functions
- Multidimensional Theta Functions
- Jacobian Elliptic Functions
- Weierstrass Elliptic and Modular Functions
- Bernoulli and Euler Polynomials
- Zeta and Related Functions
- Combinatorial Analysis
- Functions of Number Theory
- Mathieu Functions and Hill’s Equation
- Lamé Functions
- Spheroidal Wave Functions
- Heun Functions
- Painlevé Transcendents
- Coulomb Functions
- 3j,6j,9j Symbols
- Functions of Matrix Argument
- Integrals with Coalescing Saddles