Represent Functions in Terms of MeijerG: New in Wolfram Language 11

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Represent Functions in Terms of MeijerG

Represent Sin in terms of MeijerG.

In[1]:=

MeijerGReduce[Sin[x], x]

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Recover the original expression.

In[2]:=

MeijerGReduce[Sin[x], x];
Activate[%]

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Create a gallery of MeijerG representations.

show complete Wolfram Language input

In[3]:=

flist = {E^(-x), Sin[x], 
     Cos[x], Sinh[x], Cosh[x], BesselJ[n, x], BesselK[n, x], 
  AiryAi[x], AiryBi[x], Hypergeometric2F1[a, b, c, x], 
  UnitStep[x - 1], UnitBox[x]}; TraditionalForm @
 ReplaceAll[
  Grid[Map[Style[#, ScriptLevel -> 0] &, 
    Join[{{HoldForm[f[x]], Text["MeijerG Representation"]}}, 
     Transpose[{flist, Map[MeijerGReduce[#, x] &, flist]}]], {2}], 
   Background -> {None, {{None, GrayLevel[.9]}}, {{1, 1} -> 
       Hue[.6, .4, 1], {1, 2} -> Hue[.6, .4, 1]}}, 
   BaseStyle -> {FontFamily -> Times, FontSize -> 13}, 
   Dividers -> All, FrameStyle -> Hue[.6, .4, .8], Spacings -> {2, 1}],
  Inactive[MeijerG][args__] :> HoldForm[MeijerG[args]]]

Out[3]//TraditionalForm=