D[EllipticPi[n, z, m], {m, p}] == (((ArcTanh[Sqrt[-1 + n] Tan[z]] Sqrt[Cos[z]^2] Sec[z])/Sqrt[-1 + n]) Hypergeometric2F1Regularized[1/2, 1, 1 - p, m/n] - ((m Sin[z])/(4 n)) Sum[(((k + 1)! Pochhammer[3/2, k] m^k)/ (2^k (k - p + 1)!)) Sum[(1/(k - j)!) ((n - 2)/n)^j Sum[((-1)^(i + j - 1)/(i! (j - i + 1)!)) (Sum[((Binomial[-1 + i, 2 q] Pochhammer[1/2, q])/q!) (n/(2 - n))^(2 q) ((2 ArcSin[Sin[z]])/Sin[z] + (Sqrt[Cos[z]^2]/ Cos[2 z]) Sum[((p - 1)! Cos[2 z]^(2 p))/Pochhammer[1/2, p], {p, 1, q}]), {q, 0, Floor[(i - 1)/2]}] + ((2 n Sqrt[Cos[z]^2])/(2 - n)) Sum[q! Binomial[-1 + i, 1 + 2 q] Cos[2 z]^(2 q) (n/(2 - n))^(2 q) Sum[Tan[2 z]^(2 p)/ ((q - p)! Pochhammer[3/2, p]), {p, 0, q}], {q, 0, -1 + Floor[i/2]}]), {i, 0, 1 + j}], {j, 0, k}], {k, 0, Infinity}])/ m^p /; Element[p, Integers] && p >= 0

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type='integer'> -2 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> j </ci> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> i </ci> <ci> j </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> i </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> 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type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <factorial /> <ci> q </ci> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> q </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> q </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> q </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> p </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> q </ci> </uplimit> <apply> <times /> <apply> <power /> 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2007-05-02