Re: Deleting Integrate[] transformation rule (some progress)

*To*: mathgroup at smc.vnet.net*Subject*: [mg87680] Re: Deleting Integrate[] transformation rule (some progress)*From*: UHAP023 at alpha1.rhbnc.ac.uk*Date*: Tue, 15 Apr 2008 05:54:51 -0400 (EDT)*Organization*: Low Temperature Physics, RHUL*References*: <ftq5ab$it$1@smc.vnet.net> <ftscv1$b81$1@smc.vnet.net> <ftv91s$7ur$1@smc.vnet.net>

Dear All, Some progress on my original query. I tried the following where the formulae below are expressions which integrate to elliptic integrals of the first kind and are from mathematical handbooks. Unprotect[Integrate]; Integrate[1/Sqrt[1 - m_*Sin[phi_]^2], phi_] := HoldForm[Integrate[1/Sqrt[1 - m*Sin[phi]^2], phi]] Integrate[1/Sqrt[(1 - v_^2)*(1 - k_^2*v_^2)], v_] := HoldForm[Integrate[1/Sqrt[(1 - v^2)*(1 - k^2*v^2)], v]] Protect[Integrate]; Subsequent attempts to integrate (eg. [Integrate[1/Sqrt[1 - a*Sin[b]^2], b]) do indeed leave the integral undone as required. However more involved expressions such as; In[52]:= Integrate[Sqrt[Rvt^2 + (4*R^4)/Rx^4], R] // InputForm Out[52]//InputForm= (R*Sqrt[Rvt^2 + (4*R^4)/Rx^4])/3 - (I/3*Sqrt[2]*Rvt^2*Sqrt[Rvt^2 + (4*R^4)/Rx^4]* Sqrt[1 - (2*I*R^2)/(Rvt*Rx^2)]* Sqrt[1 + (2*I*R^2)/(Rvt*Rx^2)]*Rx^4* EllipticF[I*ArcSinh[Sqrt[2]*R*Sqrt[I/(Rvt*Rx^2)]], -1])/(Sqrt[I/(Rvt*Rx^2)]*(4*R^4 + Rvt^2*Rx^4)) still produce the unwanted EllipticF[]. My question is, is this; (a) because my above HoldForm[] argument expressions are failing to pattern-match the intermediate expressions produced by Integrate[], which it then uses to produce results containing calls to EllipticF[], (b) because Mathematica knows more expressions than I entered above from my handbook which it can integrate up to EllipticF[], or (c) something else? Any ideas? Thanks Tom. Ps. The Email address in the header is just a spam-trap. -- Tom Crane, Dept. Physics, Royal Holloway, University of London, Egham Hill, Egham, Surrey, TW20 0EX, England. Email: T.Crane at rhul dot ac dot uk Fax: +44 (0) 1784 472794

**Follow-Ups**:**Re: Re: Deleting Integrate[] transformation rule (some***From:*Daniel Lichtblau <danl@wolfram.com>