Rule: Q[2, 6, 9, 18, 36, 72]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^8-7\cdot t^6+\frac{15}{4}\cdot t^4-\frac{5}{8}\cdot t^2+\frac{1}{64}$
• $P_3$:
  $4\cdot t^{17}-16\cdot t^{15}+\frac{105}{4}\cdot t^{13}-\frac{91}{4}\cdot t^{11}+\frac{715}{64}\cdot t^9-\frac{99}{32}\cdot t^7+\frac{231}{512}\cdot t^5-\frac{15}{512}\cdot t^3+\frac{9}{16384}\cdot t$
• $P_4$:
  $4\cdot t^{35}-34\cdot t^{33}+132\cdot t^{31}-310\cdot t^{29}+\frac{31465}{64}\cdot t^{27}-\frac{71253}{128}\cdot t^{25}+\frac{118755}{256}\cdot t^{23}-\frac{148005}{512}\cdot t^{21}+\frac{2220075}{16384}\cdot t^{19}-\frac{1562275}{32768}\cdot t^{17}+\frac{408595}{32768}\cdot t^{15}-\frac{156009}{65536}\cdot t^{13}+\frac{676039}{2097152}\cdot t^{11}-\frac{124355}{4194304}\cdot t^9+\frac{14535}{8388608}\cdot t^7-\frac{969}{16777216}\cdot t^5+\frac{969}{1073741824}\cdot t^3-\frac{9}{2147483648}\cdot t$
• $P_5$:
  $4\cdot t^{71}-70\cdot t^{69}+\frac{1173}{2}\cdot t^{67}-\frac{12529}{4}\cdot t^{65}+\frac{47905}{4}\cdot t^{63}-\frac{279279}{8}\cdot t^{61}+\frac{2581215}{32}\cdot t^{59}-\frac{9706503}{64}\cdot t^{57}+\frac{3872894697}{16384}\cdot t^{55}-\frac{10143295635}{32768}\cdot t^{53}+\frac{45088585113}{131072}\cdot t^{51}-\frac{85675031325}{262144}\cdot t^{49}+\frac{279871768995}{1048576}\cdot t^{47}-\frac{394447695285}{2097152}\cdot t^{45}+\frac{961830587025}{8388608}\cdot t^{43}-\frac{1015828093665}{16777216}\cdot t^{41}+\frac{29749251314475}{1073741824}\cdot t^{39}-\frac{23576679383985}{2147483648}\cdot t^{37}+\frac{32308782859535}{8589934592}\cdot t^{35}-\frac{19090095135475}{17179869184}\cdot t^{33}+\frac{9691894453395}{34359738368}\cdot t^{31}-\frac{4207965378925}{68719476736}\cdot t^{29}+\frac{3106243534261}{274877906944}\cdot t^{27}-\frac{967428110493}{549755813888}\cdot t^{25}+\frac{8061900920775}{35184372088832}\cdot t^{23}-\frac{1735881645069}{70368744177664}\cdot t^{21}+\frac{609590544255}{281474976710656}\cdot t^{19}-\frac{85794224747}{562949953421312}\cdot t^{17}+\frac{18941582087}{2251799813685248}\cdot t^{15}-\frac{1594920705}{4503599627370496}\cdot t^{13}+\frac{197466373}{18014398509481984}\cdot t^{11}-\frac{8544965}{36028797018963968}\cdot t^9+\frac{15380937}{4611686018427387904}\cdot t^7-\frac{250971}{9223372036854775808}\cdot t^5+\frac{3885}{36893488147419103232}\cdot t^3-\frac{9}{73786976294838206464}\cdot t$
• $P_6$:
  $4\cdot t^{143}-142\cdot t^{141}+\frac{4935}{2}\cdot t^{139}-\frac{111895}{4}\cdot t^{137}+\frac{7445813}{32}\cdot t^{135}-\frac{96902703}{64}\cdot t^{133}+\frac{2054618181}{256}\cdot t^{131}-\frac{18243038385}{512}\cdot t^{129}+\frac{138432467745}{1024}\cdot t^{127}-\frac{911603435743}{2048}\cdot t^{125}+\frac{10544666607475}{8192}\cdot t^{123}-\frac{54078355130475}{16384}\cdot t^{121}+\frac{991436510725375}{131072}\cdot t^{119}-\frac{4087419695715125}{262144}\cdot t^{117}+\frac{30480472588047075}{1048576}\cdot t^{115}-\frac{103255554426174975}{2097152}\cdot t^{113}+\frac{81675143551104405225}{1073741824}\cdot t^{111}-\frac{230952640750112271375}{2147483648}\cdot t^{109}+\frac{1198754182941058932375}{8589934592}\cdot t^{107}-\frac{2862372619561576928631}{17179869184}\cdot t^{105}+\frac{25207345972268080694073}{137438953472}\cdot t^{103}-\frac{51263719857655527636843}{274877906944}\cdot t^{101}+\frac{192907440596989876725825}{1099511627776}\cdot t^{99}-\frac{336253681040602907652525}{2199023255552}\cdot t^{97}+\frac{2174440470729232136152995}{17592186044416}\cdot t^{95}-\frac{3263487966993620668209453}{35184372088832}\cdot t^{93}+\frac{9101174395566303271577601}{140737488355328}\cdot t^{91}-\frac{11797818660919282018711705}{281474976710656}\cdot t^{89}+\frac{56896869305615650720782065}{2251799813685248}\cdot t^{87}-\frac{63823444699342773417225099}{4503599627370496}\cdot t^{85}+\frac{133245437179329649765785733}{18014398509481984}\cdot t^{83}-\frac{129441685047461832187544633}{36028797018963968}\cdot t^{81}+\frac{7489126063460291719422225195}{4611686018427387904}\cdot t^{79}-\frac{6299207589822866171864557965}{9223372036854775808}\cdot t^{77}+\frac{9856407169958131774799837757}{36893488147419103232}\cdot t^{75}-\frac{7169470484045561120594901645}{73786976294838206464}\cdot t^{73}+\frac{19384123901308368955682511855}{590295810358705651712}\cdot t^{71}-\frac{12167099746085197487969447325}{1180591620717411303424}\cdot t^{69}+\frac{14172798413265081085787648175}{4722366482869645213696}\cdot t^{67}-\frac{7652272842913087736428935315}{9444732965739290427392}\cdot t^{65}+\frac{7652272842913087736428935315}{37778931862957161709568}\cdot t^{63}-\frac{3538927033438138846612765965}{75557863725914323419136}\cdot t^{61}+\frac{3023453067783283888562727225}{302231454903657293676544}\cdot t^{59}-\frac{1191141652999585248291693825}{604462909807314587353088}\cdot t^{57}+\frac{1728238252897580051157766677}{4835703278458516698824704}\cdot t^{55}-\frac{576079417632526683719255559}{9671406556917033397649408}\cdot t^{53}+\frac{352190522403558904243626513}{38685626227668133590597632}\cdot t^{51}-\frac{98495923681627024108493925}{77371252455336267181195264}\cdot t^{49}+\frac{1608766753466574727105400775}{9903520314283042199192993792}\cdot t^{47}-\frac{373593310525750221267655905}{19807040628566084398385987584}\cdot t^{45}+\frac{157386118051273497470203977}{79228162514264337593543950336}\cdot t^{43}-\frac{29964086991418926463334217}{158456325028528675187087900672}\cdot t^{41}+\frac{20543939241608294063490015}{1267650600228229401496703205376}\cdot t^{39}-\frac{3156346460301004748299005}{2535301200456458802993406410752}\cdot t^{37}+\frac{865072733563979079163431}{10141204801825835211973625643008}\cdot t^{35}-\frac{105151844018502053544891}{20282409603651670423947251286016}\cdot t^{33}+\frac{45065076007929451519239}{162259276829213363391578010288128}\cdot t^{31}-\frac{4225702831959506948265}{324518553658426726783156020576256}\cdot t^{29}+\frac{687905112179454619485}{1298074214633706907132624082305024}\cdot t^{27}-\frac{48146499376867112949}{2596148429267413814265248164610048}\cdot t^{25}+\frac{11463452232587407845}{20769187434139310514121985316880384}\cdot t^{23}-\frac{572832987328582695}{41538374868278621028243970633760768}\cdot t^{21}+\frac{47322945452007225}{166153499473114484112975882535043072}\cdot t^{19}-\frac{1585777713559325}{332306998946228968225951765070086144}\cdot t^{17}+\frac{5391644226101705}{85070591730234615865843651857942052864}\cdot t^{15}-\frac{110247837145215}{170141183460469231731687303715884105728}\cdot t^{13}+\frac{3340843549855}{680564733841876926926749214863536422912}\cdot t^{11}-\frac{35616668975}{1361129467683753853853498429727072845824}\cdot t^9+\frac{992414925}{10889035741470030830827987437816582766592}\cdot t^7-\frac{4027191}{21778071482940061661655974875633165533184}\cdot t^5+\frac{15549}{87112285931760246646623899502532662132736}\cdot t^3-\frac{9}{174224571863520493293247799005065324265472}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.