Rule: Q[1, 84]

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^{85}-3570\cdot t^{83}+\frac{6074355}{2}\cdot t^{81}-1640075850\cdot t^{79}+\frac{2526536846925}{4}\cdot t^{77}-\frac{739264681410255}{4}\cdot t^{75}+\frac{683819830304485875}{16}\cdot t^{73}-\frac{64181375501435317125}{8}\cdot t^{71}+\frac{159490718121066763055625}{128}\cdot t^{69}-\frac{20786956928445701451583125}{128}\cdot t^{67}+\frac{9191992353758689181890057875}{512}\cdot t^{65}-\frac{54316318454028617892986705625}{32}\cdot t^{63}+\frac{35359923313572630248334345361875}{256}\cdot t^{61}-\frac{2488794602455304359786609692778125}{256}\cdot t^{59}+\frac{608332509257289394227841312049053125}{1024}\cdot t^{57}-\frac{16181644746243897886460578900504813125}{512}\cdot t^{55}+\frac{24029742448172188361393959667249647490625}{16384}\cdot t^{53}-\frac{973911326281802222411790482984412183590625}{16384}\cdot t^{51}+\frac{137970771223255314841670318422791726008671875}{65536}\cdot t^{49}-\frac{1067458072095712172722396674113178090698671875}{16384}\cdot t^{47}+\frac{230784435187092971742582160943269103209052859375}{131072}\cdot t^{45}-\frac{5439918829410048619646579507948486004213388828125}{131072}\cdot t^{43}+\frac{446567882087024900321896481425225714709517282890625}{524288}\cdot t^{41}-\frac{3980278949036526285477772986616142239802219260546875}{262144}\cdot t^{39}+\frac{983128900412021992513009927694187133231148157355078125}{4194304}\cdot t^{37}-\frac{13095276953488132940273292236886572614638893455969640625}{4194304}\cdot t^{35}+\frac{599360752871187623035585298534423900439241662023225859375}{16777216}\cdot t^{33}-\frac{732552031287007094821270920430962544981295364695053828125}{2097152}\cdot t^{31}+\frac{48662384935494042727412996857199654773757477797600004296875}{16777216}\cdot t^{29}-\frac{340636694548458299091890978000397583416302344583200030078125}{16777216}\cdot t^{27}+\frac{7970898652433924198750248885209303451941474863246880703828125}{67108864}\cdot t^{25}-\frac{19284432223630461771169956980345088996632600475597292025390625}{33554432}\cdot t^{23}+\frac{4878961352578506828105999116027307516148047920326114882423828125}{2147483648}\cdot t^{21}-\frac{15523967940022521725791815369177796642289243382855820080439453125}{2147483648}\cdot t^{19}+\frac{156152853984932424418258848713494307401850624615785013750302734375}{8589934592}\cdot t^{17}-\frac{75845671935538606146011440803697235023756017670524149535861328125}{2147483648}\cdot t^{15}+\frac{884866172581283738370133476043134408610486872822781744585048828125}{17179869184}\cdot t^{13}-\frac{932696776504596372876627177450871403670513190272661838886943359375}{17179869184}\cdot t^{11}+\frac{2699911721460673710958657618936733010625169761315600059935888671875}{68719476736}\cdot t^9-\frac{623056551106309317913536373600784540913500714149753859985205078125}{34359738368}\cdot t^7+\frac{2616837514646499135236852769123295071836702999428966211937861328125}{549755813888}\cdot t^5-\frac{319126526176402333565469849893084764858134512125483684382666015625}{549755813888}\cdot t^3+\frac{45589503739486047652209978556154966408304930303640526340380859375}{2199023255552}\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.