FANDOM


$ \begin{align} &P(1,2^{12},24,(0,0,768,512,0,128,0,0,0,0,0,-16,0,-16,-12,0,0,0,0,2,0,-1,0)) \\ &=2^7\pi \end{align} $

$ P(1,-2^{10},20,(0,512,0,0,-160,-128,0,0,0,-8,0,0,0,-8,-5,0,0,2,0,0))=2^6\pi $

$ 64P(1,-2^{10},4,(32,8,1,0))+4P(1,-2^6,4,(8,4,1,0))=\pi $

$ P(1,-2^6,12,(0,32,24,0,0,4,0,0,3,2,0,0))=8\pi $

$ -2P(2,2,2(0,2))+P(2,-4,4,(2,-1,-1))=\frac{\pi^2}{8} $

$ \begin{align} &P(2,2^{12},24,(0,2^{10},0,-3\cdot2^9,0,-2^9,0,-3\cdot2^7,0,2^6,0,0,0,2^4,0,-3\cdot2^3,0,-8,0, \\ &-6,0,1,0,0))=\frac{2^7}{9}\pi^2 \end{align} $

$ P(2,2^{12},12,(2^{10},-3\cdot2^9,-2^9,-3\cdot2^7,2^6,0,2^4,-3\cdot2^3,-8,-6,1,0))=\frac{2^9}{9}\pi^2 $

$ \begin{align} &P(2,2^{12},24,(0,0,3\cdot2^9,0,-2^{10},0,-3\cdot2^8,0,-3\cdot2^8,-3\cdot2^6,0,0,-2^6,0,0,-3\cdot2^3, \\ &-3\cdot2^4,0,-12,0,-4,3,0,0,0))=-\frac{2^6}{9}\pi^2 \end{align} $

$ P(2,-2^6,12,(32,-64,-48,-8,0,4,12,8,0,-1,0))=\frac{20}{9}\pi $

$ -4P(2,2,1(1))+P(2,-8,3,(8,-4,-1))=\frac{2\pi^2}{9} $

$ \begin{align} &P(2,2^{60},120,(0,0,0,0,5\cdot2^{55},-3\cdot2^{55},0,-2^{57},0,0,0,3\cdot2^{52},0,0,-5\cdot2^{50},-2^{53}, \\ &0,-3\cdot2^{49},0,-5\cdot2^{48},0,0,0,-5\cdot2^{46},-5\cdot2^{45},0,0,0,0,-3\cdot2^{43},0,-2^{45},0,0,5\cdot2^{40}, \\ &3\cdot2^{40},0,0,0,-3\cdot2^{38},0,3\cdot2^{37},0,0,5\cdot2^{35},0,0,-5\cdot2^{34},0,0,0,0,0,-3\cdot2^{31}, \\ &-5\cdot2^{30},-2^{33},0,0,0,-2^{29},0,0,0,-2^{29},-5\cdot2^{25},-3\cdot2^{25},0,0,0,0,0,-5\cdot2^{22},0,0, \\ &5\cdot2^{20},0,0,-3\cdot2^{19},0,-3\cdot2^{18},0,0,0,3\cdot2^{16},5\cdot2^{15},0,0,-2^{17},0,-3\cdot2^{13}, \\ &0,0,0,0,-5\cdot2^{10},-5\cdot2^{10},0,0,0,-5\cdot2^8,0,-3\cdot2^7,0,-2^9,-5\cdot2^5,0,0,3\cdot2^4,0,0,0, \\ &-2^5,0,-6,5,0,0,0,0,0))=\frac{2^{43}}{45}\pi^2 \end{align} $

$ \begin{align} &P(2,2^{12},24,(0,5\cdot2^{11},-23\cdot2^9,-5\cdot2^{11},-3^2\cdot2^8,-2^9,0,-3^2\cdot2^6,5\cdot2^7,2^7,2^9,0, \\ &3^2\cdot2^5,23\cdot2^3,0,0,4,8,-40,-9,18,-2,0))=256\pi\log2 \end{align} $

$ \begin{align} &P(2,2^{12},24,(2^{11},-2^{12},-3^2\cdot2^9,0,-2^9,-5\cdot2^8,-2^8,-7\cdot2^6,-2^8,2^6,0,-2^5,2^6, \\ &7\cdot2^3,0,8,20,4,0,7,4,-1,0))=256\pi\log2 \end{align} $

$ \begin{align} &P(2,-2^{10},20,(2^9,-2^{11},2^8,3\cdot2^8,2^9,-2^6,0,2^5,3^2\cdot2^3,2^4,0,-8, \\ &2^5,21,0,2,-8,1,0))=32\pi\log2 \end{align} $

$ P(2,-2^6,12,(2^5,-2^5,-2^5,0,-2^3,-2^4,-4,0,-4,-2,1,0))=\frac{2^6}{3}\text{G} $

$ P(2,2^6,6,(2^6,-5\cdot2^5,-7\cdot2^3,-5\cdot2^3,4,-1))=2^5\log2 $

$ \frac{9}{8}P(2,2^6,6,(16,0,-8,0,1,0))+\frac{3}{64}P(2,2^6,1,(1))-\frac{27}{4}P(2,4,1,(1))=2^5\log2 $

$ 24P(2,-4,4,(2,-2,1,0))-P(2,-2^6,4,(8,4,1,0))=2^5\text{G} $

$ P(2,-2^6,12,(32,-56,0,-8,-36,-4,-7,0,10,0))-16P(2,-4,2,(1,0))=4\pi\log2 $

$ \begin{align} &P(2,2^{12},12,(2^{13},0,-3^2\cdot2^9,0,2^9,3^2\cdot2^6,0,0,-40,0,0,9)) \\ &+2^{10}P(2,16,4,(-4,0,1,0))-5\cdot2^9P(2,4,1,(1))=2^{11} \end{align} $

$ \begin{align} &5\cdot2^3P(3,-2^6,12,(32,-192,88,-8,84,-4,11,-2,1,0))+P(3,-2^{10},4,(32,8,1,0)) \\ &=2^4\pi^3 \end{align} $

$ \begin{align} &8P(3,-2^6,12,(7\cdot2^5,-37\cdot2^6,13\cdot17\cdot2^3,-7\cdot2^3,5\cdot71\cdot2^2,-7\cdot2^2,0, \\ &13\cdot17,-37\cdot2^2,7,0))+3P(3,-2^{10},4,(32,8,1,0))=64\pi\log^22 \end{align} $

$ 4P(3,2^4,8,(16,-88,-8,92,-4,-22,2,27))-P(3,-8,1,(1))=21\zeta(3) $

$ \begin{align} &9P(3,2^{12},24,(0,2^{11},-15\cdot2^9,2^{11},0,11\cdot2^8,3\cdot2^{10},15\cdot2^6,2^7,0,5\cdot2^6, \\ &0,2^5,15\cdot2^8,3\cdot2^6,11\cdot2^2,0,8,-15,2,0,0)) \end{align} $

$ \begin{align} &27P(5,2^{12},24,(782336,-54083584,296023040,-118439936,-195584,245927936, \\ &97792,36202086,-37002880,-3380224,-24448,-58359488,-12224,-845056, \\ &-4625360,226263043056,3843634,-1528,-462656,578170,-52816,382, \\ &1196875))+41024P(5,-2^{10},4,(-128,0,4,1))=16168\pi^4\log2 \end{align} $

$ \begin{align} &3P(5,2^{12},24,(29143040,-2536849408,16339911680,-7170572288,-7285760, \\ &17248845824,3642880,25002508288,-2042488960,-158553088,-910720, \\ &-3705698240,-455360,-39638272,-255311120,1562656768,113840, \\ &269513216,-56920,-28010048,31913890,-2477392,14230,78709375)) \\ &+302244P(5,-2^{10},4,(-128,0,4,1))=129344\pi^2\log^32 \end{align} $

$ \begin{align} &P(5,2^{12},24,(126976,-6610944,33418240,-12722176,-31744,25829376 \\ &,15782,38170624,-4177280,-413184,-3968,-6323008,-1984,-103296, \\ &-522160,2385564,496,403584,-248,-49696,65270,-6456,62,128125)) \\ &+1476P(5,-2^{10},4,(-128,0,4,1))=250604\zeta(5) \end{align} $

$ \begin{align} &P(5,2^{12},24,(11399168,-1071480832,7344051200,-3072770048,-2849792, \\ &9616483328,1424896,13679460352,-918006400,-66067552,-356224, \\ &-1886951744,-178112,-16741888,-114750800,854966272,44528,150257552, \\ &-22264,-12003008,14343850,-1046368,5566,41307505)) \\ &+52796P(5,-2^{10},4,(-128,0,4,1))=64672\log^52 \end{align} $