Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

WolframAlphaMath/SpecialFunctionsAndCalculus

(1.4) current version: 1.18.1 »

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`"]

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`]], List[List[30.928985595703125`, 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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

Wolfram|Alpha Math Team

Version History

  • 1.18.1 – 30 June 2025
  • 1.18 – 23 June 2025
  • 1.17 – 24 March 2025
  • 1.16 – 18 February 2025
  • 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

License Information

MIT License

Paclet Source

Source Metadata

  • Source: https://stash.wolfram.com/users/pacoj/repos/specialfunctionsandcalculus/browse

See Also