Verifying DLMF with Maple and Mathematica: Difference between revisions
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# [[Results of Incomplete Gamma and Related Functions|Incomplete Gamma and Related Functions]] | # [[Results of Incomplete Gamma and Related Functions|Incomplete Gamma and Related Functions]] | ||
# [[Results of Airy and Related Functions|Airy and Related Functions]] | # [[Results of Airy and Related Functions|Airy and Related Functions]] | ||
# [[Results of Bessel Functions|Bessel Functions]] | # [[Results of Bessel Functions I|Bessel Functions I]] & [[Results of Bessel Functions II|Bessel Functions II]] | ||
# [[Results of Struve and Related Functions|Struve and Related Functions]] | # [[Results of Struve and Related Functions|Struve and Related Functions]] | ||
# [[Results of Parabolic Cylinder Functions|Parabolic Cylinder Functions]] | # [[Results of Parabolic Cylinder Functions|Parabolic Cylinder Functions]] | ||
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# [[Results of Generalized Hypergeometric Functions and Meijer G-Function|Generalized Hypergeometric Functions and Meijer ''G''-Function]] | # [[Results of Generalized Hypergeometric Functions and Meijer G-Function|Generalized Hypergeometric Functions and Meijer ''G''-Function]] | ||
# [[Results of q-Hypergeometric and Related Functions|''q''-Hypergeometric and Related Functions]] | # [[Results of q-Hypergeometric and Related Functions|''q''-Hypergeometric and Related Functions]] | ||
# [[Results of Orthogonal Polynomials|Orthogonal Polynomials]] | # [[Results of Orthogonal Polynomials I|Orthogonal Polynomials I]] & [[Results of Orthogonal Polynomials II|Orthogonal Polynomials II]] | ||
# [[Results of Elliptic Integrals|Elliptic Integrals]] | # [[Results of Elliptic Integrals I|Elliptic Integrals I]] & [[Results of Elliptic Integrals II|Elliptic Integrals II]] | ||
# [[Results of Theta Functions|Theta Functions]] | # [[Results of Theta Functions|Theta Functions]] | ||
# [[Results of Multidimensional Theta Functions|Multidimensional Theta Functions]] | # [[Results of Multidimensional Theta Functions|Multidimensional Theta Functions]] | ||
Revision as of 13:26, 15 October 2020
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
- 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 I & Bessel Functions II
- 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 I & Orthogonal Polynomials II
- Elliptic Integrals I & Elliptic Integrals II
- 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