Rule: Q[8, 32, 80]

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.

• $P_1$:
  $128\cdot t^8-256\cdot t^6+160\cdot t^4-32\cdot t^2+1$
• $P_2$:
  $128\cdot t^{40}-1280\cdot t^{38}+5920\cdot t^{36}-16800\cdot t^{34}+32725\cdot t^{32}-46376\cdot t^{30}+49445\cdot t^{28}-40455\cdot t^{26}+\frac{13147875}{512}\cdot t^{24}-\frac{3251625}{256}\cdot t^{22}+\frac{10015005}{2048}\cdot t^{20}-\frac{2982525}{2048}\cdot t^{18}+\frac{21729825}{65536}\cdot t^{16}-\frac{928625}{16384}\cdot t^{14}+\frac{928625}{131072}\cdot t^{12}-\frac{81719}{131072}\cdot t^{10}+\frac{1225785}{33554432}\cdot t^8-\frac{21945}{16777216}\cdot t^6+\frac{3325}{134217728}\cdot t^4-\frac{25}{134217728}\cdot t^2+\frac{1}{4294967296}$
• $P_3$:
  $128\cdot t^{120}-3840\cdot t^{118}+56160\cdot t^{116}-533600\cdot t^{114}+3703575\cdot t^{112}-20018628\cdot t^{110}+\frac{175455665}{2}\cdot t^{108}-\frac{640823535}{2}\cdot t^{106}+\frac{509454710325}{512}\cdot t^{104}-\frac{682842699825}{256}\cdot t^{102}+\frac{12790264533813}{2048}\cdot t^{100}-\frac{26401922202825}{2048}\cdot t^{98}+\frac{1549238718889225}{65536}\cdot t^{96}-\frac{317421304732875}{8192}\cdot t^{94}+\frac{3739753431232875}{65536}\cdot t^{92}-\frac{4969716781949465}{65536}\cdot t^{90}+\frac{1531055054746739025}{16777216}\cdot t^{88}-\frac{836790226951815675}{8388608}\cdot t^{86}+\frac{6663329584986680375}{67108864}\cdot t^{84}-\frac{6052206079537146375}{67108864}\cdot t^{82}+\frac{160795011121142904891}{2147483648}\cdot t^{80}-\frac{30550278688240234455}{536870912}\cdot t^{78}+\frac{170208695548767020535}{4294967296}\cdot t^{76}-\frac{108716894288208428625}{4294967296}\cdot t^{74}+\frac{32627147941383440635125}{2199023255552}\cdot t^{72}-\frac{8778420014544849922461}{1099511627776}\cdot t^{70}+\frac{34697028371728007467665}{8796093022208}\cdot t^{68}-\frac{15738715776741617087085}{8796093022208}\cdot t^{66}+\frac{209686617025532724545325}{281474976710656}\cdot t^{64}-\frac{5005781308301842230525}{17592186044416}\cdot t^{62}+\frac{14023603635553753567293}{140737488355328}\cdot t^{60}-\frac{4498328821118184815895}{140737488355328}\cdot t^{58}+\frac{675976140118941772788585}{72057594037927936}\cdot t^{56}-\frac{90648141395260390986975}{36028797018963968}\cdot t^{54}+\frac{177452107163635594394475}{288230376151711744}\cdot t^{52}-\frac{39546469596467361036483}{288230376151711744}\cdot t^{50}+\frac{256319710347473636347575}{9223372036854775808}\cdot t^{48}-\frac{11768505098988532310325}{2305843009213693952}\cdot t^{46}+\frac{15635947082738293891125}{18446744073709551616}\cdot t^{44}-\frac{2341184859175439382875}{18446744073709551616}\cdot t^{42}+\frac{80630406550002132346215}{4722366482869645213696}\cdot t^{40}-\frac{4854254176366290771075}{2361183241434822606848}\cdot t^{38}+\frac{4166716344304642749775}{18889465931478580854784}\cdot t^{36}-\frac{396410645864078062875}{18889465931478580854784}\cdot t^{34}+\frac{1064049628371999010875}{604462909807314587353088}\cdot t^{32}-\frac{9773492882824287211}{75557863725914323419136}\cdot t^{30}+\frac{4995851238576457035}{604462909807314587353088}\cdot t^{28}-\frac{275201365226158665}{604462909807314587353088}\cdot t^{26}+\frac{3312609025870428375}{154742504910672534362390528}\cdot t^{24}-\frac{65699920317637125}{77371252455336267181195264}\cdot t^{22}+\frac{17344778963856201}{618970019642690137449562112}\cdot t^{20}-\frac{468244956398505}{618970019642690137449562112}\cdot t^{18}+\frac{324169585198965}{19807040628566084398385987584}\cdot t^{16}-\frac{1369344910725}{4951760157141521099596496896}\cdot t^{14}+\frac{139854530725}{39614081257132168796771975168}\cdot t^{12}-\frac{1290964899}{39614081257132168796771975168}\cdot t^{10}+\frac{8299060065}{40564819207303340847894502572032}\cdot t^8-\frac{16177505}{20282409603651670423947251286016}\cdot t^6+\frac{269925}{162259276829213363391578010288128}\cdot t^4-\frac{225}{162259276829213363391578010288128}\cdot t^2+\frac{1}{5192296858534827628530496329220096}$

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.