       Re: Can't integrate sqrt(a+b*cos(t)+c*cos(2t))

• To: mathgroup at smc.vnet.net
• Subject: [mg90805] Re: Can't integrate sqrt(a+b*cos(t)+c*cos(2t))
• From: Valeri Astanoff <astanoff at gmail.com>
• Date: Fri, 25 Jul 2008 06:11:51 -0400 (EDT)
• References: <g6710s\$sb6\$1@smc.vnet.net> <g69fuv\$ihd\$1@smc.vnet.net>

```On 24 juil, 10:53, "David W.Cantrell" <DWCantr... at sigmaxi.net> wrote:
[...]
Good day,

Thank you, David (along with Alois, Kevin & Grischka)
for your advice and suggestions.

Though I still wonder why

(1/5)*Sqrt[2+4*I]*(-5*I*EllipticE[-(3/5)-(4*I)/5]+
(2+I)*Sqrt*EllipticE[-(3/5)+(4*I)/5]-
(12-4*I)*EllipticK[-(3/5)-(4*I)/5]+
(6-2*I)*Sqrt*EllipticK[8/5-(4*I)/5]+
4*I*Sqrt*EllipticPi[1/5+(2*I)/5,-(3/5)+(4*I)/5]+
(8+4*I)*EllipticPi[1-2*I,-(3/5)-(4*I)/5])

doesn't fullsimplifies to

(1/5^(3/4))*(Sqrt*(10*EllipticE[(1/10)*(5-Sqrt)]-
10*EllipticK[(1/10)*(5-Sqrt)]+(5+3*Sqrt)*
EllipticPi[(1/10)*(5-3*Sqrt),(1/10)*(5-Sqrt)]))

(I have to say I'm not very familiar with the Elliptics!)

Thanks anyway

Valeri

```

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