When I type in Wolfram Alpha, say,

cos(a+b)

or

cos(a+b)^2

or (OK this next one can easily be obtained in Mathematica, still, I have run into Bessel function expressions that cannot be simplified by Mathematica, but get a decent “alternative expression” through W|A)

D[A^mu BesselK[mu, A r], A]

I get several alternative forms of these, but I cannot seem to obtain them simply from pure Mathematica (i.e. no W|A integration stuff). Am I missing something or is Wolfram Alpha just smarter in these things? The alternative expressions have helped me quite a lot, so it would be nice to have them in my toolbox without having to access Alpha.

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Where do you type those?

– Yves Klett

Jun 12 ’14 at 13:10

@YvesKlett In W|A I think

– Öskå

Jun 12 ’14 at 13:11

@Öskå yes, indeed, missed that when writing it down 🙂

– rubenvb

Jun 12 ’14 at 13:12

You can query W|A by entering = or ==?

– Yves Klett

Jun 12 ’14 at 13:12

So @rubenvb Check #@Cos[a+b]&/@{TrigToExp,TrigExpand}

– Öskå

Jun 12 ’14 at 13:19

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1 Answer

1

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You can call Wolfram Alpha directly from the notebook,

Part[#, 2] & /@

WolframAlpha[

“cos(a+b)^2”,{{“AlternativeRepresentations:MathematicalFunctionIdentityData”, All},

“Content”},PodStates ->{“AlternativeRepresentations:MathematicalFunctionIdentityData__More”}]

it should give you all the alternate forms.

{HoldForm[Cos[a + b]^2 == Cosh[(a + b)*I]^2],

HoldForm[Cos[a + b]^2 == (1/Sec[a + b])^2],

HoldForm[Cos[a + b]^2 == Cosh[(-I)*(a + b)]^2],

HoldForm[Cos[a + b]^2 == (1/Csc[a + b + Pi/2])^2],

HoldForm[Cos[a + b]^2 == ((1/2)*(E^((-I)*(a + b)) + E^((a + b)*I)))^2],

HoldForm[Cos[a + b]^2 == (1/Csc[-a – b + Pi/2])^2],

HoldForm[Cos[a + b]^2 == (-(I/Csch[(a + b)*I + (I*Pi)/2]))^2],

HoldForm[Cos[a + b]^2 == (-(I/Csch[-((a + b)*I) + (I*Pi)/2]))^2]}