Rule: Q[41, 42, 82]

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.

• $P_1$:
  $1099511627776\cdot t^{41}-11269994184704\cdot t^{39}+53532472377344\cdot t^{37}-156371169312768\cdot t^{35}+314327181557760\cdot t^{33}-461013199618048\cdot t^{31}+510407471005696\cdot t^{29}-435347548798976\cdot t^{27}+289407177326592\cdot t^{25}-150732904857600\cdot t^{23}+61508749885440\cdot t^{21}-19570965872640\cdot t^{19}+4808383856640\cdot t^{17}-898269511680\cdot t^{15}+124759654400\cdot t^{13}-12475965440\cdot t^{11}+857722624\cdot t^9-37840704\cdot t^7+959728\cdot t^5-11480\cdot t^3+41\cdot t$
• $P_2$:
  $1099511627776\cdot t^{83}-23089744183296\cdot t^{81}+233714940379136\cdot t^{79}-1518700435865600\cdot t^{77}+7119247595536384\cdot t^{75}-25649480267202560\cdot t^{73}+73889251023912960\cdot t^{71}-174819749287428096\cdot t^{69}+346289158886522880\cdot t^{67}-582511270050136064\cdot t^{65}+841157258254483456\cdot t^{63}-1051405862951714816\cdot t^{61}+1144943744511377408\cdot t^{59}-1091650524825518080\cdot t^{57}+914790069547630592\cdot t^{55}-675652939508219904\cdot t^{53}+440707832656026624\cdot t^{51}-254179451075374080\cdot t^{49}+129699112314853200\cdot t^{47}-58547753129181120\cdot t^{45}+23364978736232595\cdot t^{43}-8232763135095345\cdot t^{41}+\frac{20451120164687415}{8}\cdot t^{39}-\frac{2791046030456775}{4}\cdot t^{37}+\frac{42719234588752995}{256}\cdot t^{35}-\frac{8915937632568603}{256}\cdot t^{33}+\frac{6464589917377977}{1024}\cdot t^{31}-\frac{126479131407559}{128}\cdot t^{29}+\frac{2172923466125125}{16384}\cdot t^{27}-\frac{248038436099363}{16384}\cdot t^{25}+\frac{190742247267145}{131072}\cdot t^{23}-\frac{7628634009535}{65536}\cdot t^{21}+\frac{128123043930959}{16777216}\cdot t^{19}-\frac{6772585417995}{16777216}\cdot t^{17}+\frac{4513717165821}{268435456}\cdot t^{15}-\frac{36003011061}{67108864}\cdot t^{13}+\frac{54249295919}{4294967296}\cdot t^{11}-\frac{895743277}{4294967296}\cdot t^9+\frac{77122435}{34359738368}\cdot t^7-\frac{241367}{17179869184}\cdot t^5+\frac{45961}{1099511627776}\cdot t^3-\frac{41}{1099511627776}\cdot t$
• $P_3$:
  $1099511627776\cdot t^{165}-45629732552704\cdot t^{163}+929637081284608\cdot t^{161}-12394244824104960\cdot t^{159}+121619218826264576\cdot t^{157}-936628203563253760\cdot t^{155}+5895480533441314816\cdot t^{153}-31186341528864817152\cdot t^{151}+141490064276953497600\cdot t^{149}-559123324742842449920\cdot t^{147}+1947892417914239713280\cdot t^{145}-6041144593358981693440\cdot t^{143}+16812281812927278612480\cdot t^{141}-42263103977227290214400\cdot t^{139}+96503676766811336114176\cdot t^{137}-201110008256784546906112\cdot t^{135}+384059423675284401348864\cdot t^{133}-674474620999287813648768\cdot t^{131}+1092603955185529381246080\cdot t^{129}-1637000119675197522246144\cdot t^{127}+2273727179167182708673704\cdot t^{125}-2933746473007789174665900\cdot t^{123}+3522770544520697598835050\cdot t^{121}-3942864756011080396228875\cdot t^{119}+\frac{131813352061572292852993725}{32}\cdot t^{117}-\frac{257386813912668677357403855}{64}\cdot t^{115}+\frac{29386943211229138140456015}{8}\cdot t^{113}-\frac{402155838579852628772047855}{128}\cdot t^{111}+\frac{10315040214824363347957397825}{4096}\cdot t^{109}-\frac{15506980846257736041275354615}{8192}\cdot t^{107}+\frac{21874023577362113304228786375}{16384}\cdot t^{105}-\frac{28965152050711527465906033085}{32768}\cdot t^{103}+\frac{2305192003408544909837207335735}{4194304}\cdot t^{101}-\frac{2692657223428169219315080827125}{8388608}\cdot t^{99}+\frac{1477501404331784302356984985425}{8388608}\cdot t^{97}-\frac{761764874166282566725744731825}{8388608}\cdot t^{95}+\frac{188946006840307861783576202590325}{4294967296}\cdot t^{93}-\frac{172004919291290640730220823991675}{8589934592}\cdot t^{91}+\frac{147098567795461258769253704868625}{17179869184}\cdot t^{89}-\frac{118152881375500340859028374406263}{34359738368}\cdot t^{87}+\frac{1425732793249340419735595117256227}{1099511627776}\cdot t^{85}-\frac{1009218474181506206459496364709153}{2199023255552}\cdot t^{83}+\frac{167550539733172478187786662543593}{1099511627776}\cdot t^{81}-\frac{208657889998088376195516566128995}{4398046511104}\cdot t^{79}+\frac{1947961493381575373652608433648327}{140737488355328}\cdot t^{77}-\frac{1064297420863342895990794378503249}{281474976710656}\cdot t^{75}+\frac{544068962287673151074451062252805}{562949953421312}\cdot t^{73}-\frac{259994034392851557111702311222895}{1125899906842624}\cdot t^{71}+\frac{3712857798639493820679777617523075}{72057594037927936}\cdot t^{69}-\frac{1545646552262523773815299120007785}{144115188075855872}\cdot t^{67}+\frac{299751844536670141742360224048047}{144115188075855872}\cdot t^{65}-\frac{27044837069501026927168432499799}{72057594037927936}\cdot t^{63}+\frac{290190374806231404457934397015897}{4611686018427387904}\cdot t^{61}-\frac{90261598634826822591905298438855}{9223372036854775808}\cdot t^{59}+\frac{25997665979627678843744143430481}{18446744073709551616}\cdot t^{57}-\frac{6920633182303037531541520613055}{36893488147419103232}\cdot t^{55}+\frac{27186184110306451224487011294549}{1180591620717411303424}\cdot t^{53}-\frac{6141954639230282476402161906231}{2361183241434822606848}\cdot t^{51}+\frac{159206468141122596829639445025}{590295810358705651712}\cdot t^{49}-\frac{120880005848089194518656232115}{4722366482869645213696}\cdot t^{47}+\frac{335029708025109233249348496345}{151115727451828646838272}\cdot t^{45}-\frac{52786055607284930371015885695}{302231454903657293676544}\cdot t^{43}+\frac{7536728223647193862457421255}{604462909807314587353088}\cdot t^{41}-\frac{971186275221425121962258925}{1208925819614629174706176}\cdot t^{39}+\frac{14391911839547928451810707663}{309485009821345068724781056}\cdot t^{37}-\frac{1489401941179385885474705757}{618970019642690137449562112}\cdot t^{35}+\frac{68500953954831444629280669}{618970019642690137449562112}\cdot t^{33}-\frac{2782414015712510036367603}{618970019642690137449562112}\cdot t^{31}+\frac{12683592305984333023810365}{79228162514264337593543950336}\cdot t^{29}-\frac{785531037711792567562899}{158456325028528675187087900672}\cdot t^{27}+\frac{41899834537508397147633}{316912650057057350374175801344}\cdot t^{25}-\frac{1903531195938647086695}{633825300114114700748351602688}\cdot t^{23}+\frac{1163182633613052965055}{20282409603651670423947251286016}\cdot t^{21}-\frac{36768056998146801525}{40564819207303340847894502572032}\cdot t^{19}+\frac{235993638505585455}{20282409603651670423947251286016}\cdot t^{17}-\frac{9615805137200691}{81129638414606681695789005144064}\cdot t^{15}+\frac{2415273922674963}{2596148429267413814265248164610048}\cdot t^{13}-\frac{28120221427077}{5192296858534827628530496329220096}\cdot t^{11}+\frac{230545201905}{10384593717069655257060992658440192}\cdot t^9-\frac{1235891331}{20769187434139310514121985316880384}\cdot t^7+\frac{123579945}{1329227995784915872903807060280344576}\cdot t^5-\frac{183803}{2658455991569831745807614120560689152}\cdot t^3+\frac{41}{2658455991569831745807614120560689152}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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