Rule: Q[1, 58]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{59}-1711\cdot t^{57}+682689\cdot t^{55}-\frac{337931055}{2}\cdot t^{53}+\frac{232834496895}{8}\cdot t^{51}-\frac{59372796708225}{16}\cdot t^{49}+\frac{2909267038703025}{8}\cdot t^{47}-\frac{449273952691138575}{16}\cdot t^{45}+\frac{222390606582113594625}{128}\cdot t^{43}-\frac{22313190860405397327375}{256}\cdot t^{41}+\frac{914840825276621290422375}{256}\cdot t^{39}-\frac{61627004684543306927543625}{512}\cdot t^{37}+\frac{6840597519984307068957342375}{2048}\cdot t^{35}-\frac{313088886491589438925355285625}{4096}\cdot t^{33}+\frac{1475990464888921640648103489375}{1024}\cdot t^{31}-\frac{45755704411556570860091208170625}{2048}\cdot t^{29}+\frac{9288407995545983884598515258636875}{32768}\cdot t^{27}-\frac{191778306260978843734945815045973125}{65536}\cdot t^{25}+\frac{1598152552174823697791215125383109375}{65536}\cdot t^{23}-\frac{21280662931591073449535654037996140625}{131072}\cdot t^{21}+\frac{446893921563412542440248734797918953125}{524288}\cdot t^{19}-\frac{3638993361302073559870596840497340046875}{1048576}\cdot t^{17}+\frac{5623898831103204592527286026223161890625}{524288}\cdot t^{15}-\frac{25674320750688542705015870989279652109375}{1048576}\cdot t^{13}+\frac{333766169758951055165206322860635477421875}{8388608}\cdot t^{11}-\frac{734285573469692321363453910293398050328125}{16777216}\cdot t^9+\frac{508351550863633145559314245587737111765625}{16777216}\cdot t^7-\frac{395384539560603557657244413234906642484375}{33554432}\cdot t^5+\frac{282417528257573969755174580882076173203125}{134217728}\cdot t^3-\frac{29215606371473169285018060091249259296875}{268435456}\cdot t$

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.