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 in 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%)

By clicking on a chapter of the DLMF below, you will see a large table that looks like this:

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
Link to DLMF	Formula	Translation to Maple	Translation to Mathematica	Symbolic Result in Maple	Symbolic Result in Mathematica	Numeric Result in Maple	Numeric Result in Mathematica

The result tables do not contain every equation with a label in the DLMF since quite a few equations were skipped (see explanations in the paper).

Translations and Evaluations of the Digital Library of Mathematical Functions

1. Algebraic and Analytic Methods
2. Asymptotic Approximations
3. Numerical Methods
4. Elementary Functions
5. Gamma Function
6. Exponential, Logarithmic, Sine, and Cosine Integrals
7. Error Functions, Dawson’s and Fresnel Integrals
8. Incomplete Gamma and Related Functions
9. Airy and Related Functions
10. Bessel Functions I & Bessel Functions II
11. Struve and Related Functions
12. Parabolic Cylinder Functions
13. Confluent Hypergeometric Functions
14. Legendre and Related Functions
15. Hypergeometric Function
16. Generalized Hypergeometric Functions and Meijer G-Function
17. q-Hypergeometric and Related Functions
18. Orthogonal Polynomials I & Orthogonal Polynomials II
19. Elliptic Integrals I & Elliptic Integrals II
20. Theta Functions
21. Multidimensional Theta Functions
22. Jacobian Elliptic Functions
23. Weierstrass Elliptic and Modular Functions
24. Bernoulli and Euler Polynomials
25. Zeta and Related Functions
26. Combinatorial Analysis
27. Functions of Number Theory
28. Mathieu Functions and Hill’s Equation
29. Lamé Functions
30. Spheroidal Wave Functions
31. Heun Functions
32. Painlevé Transcendents
33. Coulomb Functions
34. 3j,6j,9j Symbols
35. Functions of Matrix Argument
36. Integrals with Coalescing Saddles