Rule: Q[16, 27]

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.

• $P_1$:
  $65536\cdot t^{16}-3932160\cdot t^{14}+89456640\cdot t^{12}-984023040\cdot t^{10}+5535129600\cdot t^8-15498362880\cdot t^6+19372953600\cdot t^4-8302694400\cdot t^2+518918400$
• $P_2$:
  $65536\cdot t^{43}-\frac{465616115826688}{13835649}\cdot t^{41}+\frac{1618623396203167744}{235206033}\cdot t^{39}-\frac{554795812051242631168}{705618099}\cdot t^{37}+\frac{13536290773850294128640}{235206033}\cdot t^{35}-\frac{681744432346301058775040}{235206033}\cdot t^{33}+\frac{24631785131895477853757440}{235206033}\cdot t^{31}-\frac{218309697540049642449162240}{78402011}\cdot t^{29}+\frac{4337844132599596986460853760}{78402011}\cdot t^{27}-\frac{64952331525293709427881350400}{78402011}\cdot t^{25}+\frac{43234758445313884892867424000}{4611883}\cdot t^{23}-\frac{6273922392870285163861875024000}{78402011}\cdot t^{21}+\frac{40143144980085269844762019980000}{78402011}\cdot t^{19}-\frac{190399314755512917048294149850000}{78402011}\cdot t^{17}+\frac{38725704021190181844567979260000}{4611883}\cdot t^{15}-\frac{95323364301430537463510889570000}{4611883}\cdot t^{13}+\frac{161560763746224820795764841269375}{4611883}\cdot t^{11}-\frac{359617302987958212288824978870625}{9223766}\cdot t^9+\frac{245067583492026240582823058998125}{9223766}\cdot t^7-\frac{183149589532955666652388203721875}{18447532}\cdot t^5+\frac{123119907398763238284686924934375}{73790128}\cdot t^3-\frac{11692695166596478222344146615625}{147580256}\cdot t$

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.