Rule: Q[1, 86]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{87}-3741\cdot t^{85}+\frac{6677685}{2}\cdot t^{83}-\frac{7574720685}{4}\cdot t^{81}+\frac{3067761877425}{4}\cdot t^{79}-\frac{1890354868869285}{8}\cdot t^{77}+\frac{921863057718587985}{16}\cdot t^{75}-\frac{365452855024154522625}{32}\cdot t^{73}+\frac{240102525750869521364625}{128}\cdot t^{71}-\frac{66294975165656751176788125}{256}\cdot t^{69}+\frac{15552801173863073826074494125}{512}\cdot t^{67}-\frac{3126113035946477839040973319125}{1024}\cdot t^{65}+\frac{67732449112173686512554421914375}{256}\cdot t^{63}-\frac{10175497932005785366078368153751875}{512}\cdot t^{61}+\frac{1330082943969327658565958122954709375}{1024}\cdot t^{59}-\frac{151718127808767974920423623225033849375}{2048}\cdot t^{57}+\frac{60535532995698421993249025666788505900625}{16384}\cdot t^{55}-\frac{5287956852859538627057341359716525368378125}{32768}\cdot t^{53}+\frac{404822474624469123782500910760520664312503125}{65536}\cdot t^{51}-\frac{27165718691905164885404666379982307736760078125}{131072}\cdot t^{49}+\frac{798672129542011847630897191571479847460746296875}{131072}\cdot t^{47}-\frac{41112598668329276537571422099465224528812702234375}{262144}\cdot t^{45}+\frac{1850066940074817444190713994475935103796571600546875}{524288}\cdot t^{43}-\frac{72635236821198267482791945087468234727317571969296875}{1048576}\cdot t^{41}+\frac{4963407849448548277990782914310329373033367417901953125}{4194304}\cdot t^{39}-\frac{147115408657654970959646805580158162616709010266613890625}{8388608}\cdot t^{37}+\frac{3768417775615315794581722019860974473181853878367878890625}{16777216}\cdot t^{35}-\frac{83044762092263440658374985252491844871970483615884738515625}{33554432}\cdot t^{33}+\frac{391496735577813363103767787618890125825003708474885195859375}{16777216}\cdot t^{31}-\frac{6277447656678731511836276594578755465814714635890400554296875}{33554432}\cdot t^{29}+\frac{84954791620385499793517609913299157304025804739050087501484375}{67108864}\cdot t^{27}-\frac{961907479314687433145957454179613039152034111722792926226484375}{134217728}\cdot t^{25}+\frac{72143060948601557485946809063470977936402558379209469466986328125}{2147483648}\cdot t^{23}-\frac{553096800605945274058925536153277497512419614240605932580228515625}{4294967296}\cdot t^{21}+\frac{3416186121389661986834540076240831602282591735015507230642587890625}{8589934592}\cdot t^{19}-\frac{16690509335932348564248752943919491542580662476790049612568072265625}{17179869184}\cdot t^{17}+\frac{31526517634538880621358755560736817358207918011714538157073025390625}{17179869184}\cdot t^{15}-\frac{89467144638556282844396468483172049259779226790000716391693720703125}{34359738368}\cdot t^{13}+\frac{183643086363352370049024330044405785322704728674211996804002900390625}{68719476736}\cdot t^{11}-\frac{258983839743189239812726619293392774173045130181581021133850244140625}{137438953472}\cdot t^9+\frac{466170911537740631662907914728106993511481234326845838040930439453125}{549755813888}\cdot t^7-\frac{238770466885184225973684541690006021066856241972286892655110712890625}{1099511627776}\cdot t^5+\frac{56850111163139101422305843259525243111156248088639736346454931640625}{2199023255552}\cdot t^3-\frac{3966286825335286145742268134385482077522528936416725791613134765625}{4398046511104}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.