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, integral transforms and more.
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-abf695f978d0/1-6-2/71f1b914a84561da.png){kind=small} |
Get an example univariate function to work with:
| In[2]:= | ![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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myFunc = ReleaseHold[%]](https://www.wolframcloud.com/obj/resourcesystem/images/696/6962365e-7a99-4b7a-af80-abf695f978d0/1-6-2/00c6f9170b133820.png){kind=small} |
| Out[3]= |  |
Compute the (inactivated) MeijerG form of the 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 ath-order derivative of the function:
| In[5]:= | ![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[5]= |  |
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