Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Compute MeijerG forms of functions, fractional-order integro-derivatives, integral transforms and more
Contributed by: Paco Jain & Oleg Marichev
This paclet contains tools related to special functions and calculus. Operations include conversion off univariate function expressions into MeijerG forms, fractional order differentiation, and integral transforms.
Installation Instructions
To install this paclet in your Wolfram Language environment,
evaluate this code:
PacletInstall["WolframAlphaMath/SpecialFunctionsAndCalculus"]
To load the code after installation, evaluate this code:
Needs["WolframAlphaMath`SpecialFunctionsAndCalculus`"]
Details
Authors: Paco Jain and Oleg Marichev
Examples
Basic Examples
Load the paclet in the current Wolfram session:
| In[1]:= | ![Needs["WolframAlphaMath`SpecialFunctionsAndCalculus`"]](https://www.wolframcloud.com/obj/resourcesystem/images/696/6962365e-7a99-4b7a-af80-abf695f978d0/1-4/5df15b748465c2d4.png){kind=small} |
Get an example univariate function to work with:
| In[2]:= | ![myFunc = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], 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| Out[2]= |  |
Compute the MeijerG form of the function:
| In[3]:= | ![InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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| Out[3]= |  |
Compute the ath-order derivative of the logarithm function:
| In[4]:= | ![InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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| Out[4]= |  |
Compute the Mellin transform of the function:
Publisher
Version History
- 1.15 – 05 November 2024
- 1.14.9 – 16 October 2024
- 1.14.8 – 16 October 2024
- 1.14.7 – 16 October 2024
- 1.14.6 – 16 October 2024
- 1.14.5 – 15 October 2024
- 1.14.4 – 14 October 2024
- 1.14.3 – 14 October 2024
- 1.14.2 – 14 October 2024
- 1.14.1 – 08 October 2024
- 1.14 – 07 October 2024
- 1.13.2 – 27 September 2024
- 1.13.1 – 18 September 2024
- 1.13 – 18 September 2024
- 1.12.2 – 10 September 2024
- 1.12.1 – 06 September 2024
- 1.12 – 29 August 2024
- 1.11.3 – 13 August 2024
- 1.11.2 – 08 August 2024
- 1.11.1 – 05 August 2024
- 1.11 – 30 May 2024
- 1.10.1 – 04 April 2024
- 1.10 – 15 March 2024
- 1.9 – 16 January 2024
- 1.8.2 – 27 October 2023
- 1.8.1 – 27 October 2023
- 1.8 – 23 October 2023
- 1.7.10 – 02 October 2023
- 1.7.9 – 11 September 2023
- 1.7.8 – 11 September 2023
- 1.7.7 – 09 September 2023
- 1.7.6 – 11 August 2023
- 1.7.5 – 04 August 2023
- 1.7.4 – 04 August 2023
- 1.7.3 – 03 August 2023
- 1.7.2 – 14 July 2023
- 1.7.1 – 30 June 2023
- 1.7 – 17 May 2023
- 1.6.6 – 02 May 2023
- 1.6.5 – 06 April 2023
- 1.6.4 – 10 January 2023
- 1.6.3 – 10 January 2023
- 1.6.2 – 10 January 2023
- 1.6.1 – 09 January 2023
- 1.6 – 09 January 2023
- 1.5.2 – 28 December 2022
- 1.5.1 – 13 December 2022
- 1.5 – 13 December 2022
- 1.4 – 29 November 2022
- 1.3.2 – 07 November 2022
- 1.3.1 – 07 November 2022
- 1.3.0 – 04 November 2022
- 1.2.7 – 21 October 2022