GaussLaguerre Coefficients

b4caeeaa-5625-461b-9ebe-b37f17834037 3 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Coeffs from:

https://keisan.casio.com/exec/system/1280801905

GaussLaguerre.50 1 - 0.0008163265306122448979592 0.997005175362643586236 - 0.0050273455497416577264 0.989972220058020802022 - 0.0090329866868996020993 0.9789519106467198092673 - 0.013000139812211760657 0.9639894801099686121339 - 0.0169146554838637660232 0.9451453286808814137682 - 0.0207609894970159934393 0.922495378502752746657 - 0.0245237017181694943149 0.8961308490768326327616 - 0.0281876554510602491663 0.8661579081773533109677 - 0.0317381026065706387509 0.832697249796457952787 - 0.03516074908934724962954 0.795883610117728469387 - 0.0384418142109977345625 0.7558652257940530390604 - 0.041568086852368492733 0.7128032374236458598544 - 0.04452697893447274223 0.6668710408790448158956 - 0.04730657622923672285351 0.6182535892015291708338 - 0.04989568639334337604645 0.5671466479156704257289 - 0.052283884066433463416 0.5137560067830487440676 - 0.054461552866930615293 0.4582966511792997592748 - 0.0564199241232101410276 0.4009918964363984808992 - 0.058151112187474100161 0.3420724886388038436291 - 0.0596481461918334541467 0.281775675495909512023 - 0.060904998119632791003 0.2203442510330564760657 - 0.0619166070794861790183 0.1580255779484029029865 - 0.06267889968456801074686 0.0950705915726566477616 - 0.0631888064552666332142 0.0317327894426237129119 - 0.0634442741792528868443 0.0317327894426237129119 0.0634442741792528868443 0.0950705915726566477616 0.0631888064552666332142 0.158025577948402902987 0.0626788996845680107469 0.220344251033056476066 0.061916607079486179018 0.281775675495909512023 0.0609049981196327910029 0.342072488638803843629 0.059648146191833454147 0.4009918964363984808992 0.0581511121874741001609 0.458296651179299759275 0.0564199241232101410276 0.5137560067830487440676 0.054461552866930615293 0.5671466479156704257289 0.0522838840664334634156 0.6182535892015291708338 0.049895686393343376046 0.6668710408790448158956 0.047306576229236722854 0.7128032374236458598544 0.04452697893447274223 0.7558652257940530390604 0.041568086852368492733 0.795883610117728469387 0.0384418142109977345625 0.832697249796457952787 0.0351607490893472496295 0.8661579081773533109677 0.0317381026065706387509 0.8961308490768326327616 0.0281876554510602491663 0.922495378502752746657 0.024523701718169494315 0.9451453286808814137682 0.0207609894970159934393 0.9639894801099686121339 0.016914655483863766023 0.9789519106467198092673 0.013000139812211760657 0.9899722200580208020225 0.0090329866868996020993 0.9970051753626435862362 0.005027345549741657726 1 0.0008163265306122448979592 502 mat :

GaussLegendre Coefficients

Coeffs from:

https://pomax.github.io/bezierinfo/legendre-gauss.html

GaussLegendre.50 0.062176617 0.031098338 - 0.062176617 0.031098338 0.061936067 0.093174702 - 0.061936067 0.093174702 0.0614559 0.15489059 - 0.0614559 0.15489059 0.060737971 0.216007237 - 0.060737971 0.216007237 0.059785059 0.276288194 - 0.059785059 0.276288194 0.05860085 0.335500245 - 0.05860085 0.335500245 0.057189926 0.393414312 - 0.057189926 0.393414312 0.055557745 0.449806335 - 0.055557745 0.449806335 0.053710622 0.504458145 - 0.053710622 0.504458145 0.051655703 0.557158305 - 0.051655703 0.557158305 0.049400938 0.607702927 - 0.049400938 0.607702927 0.046955051 0.655896466 - 0.046955051 0.655896466 0.044327504 0.701552469 - 0.044327504 0.701552469 0.041528463 0.744494302 - 0.041528463 0.744494302 0.038568757 0.784555833 - 0.038568757 0.784555833 0.035459836 0.821582071 - 0.035459836 0.821582071 0.032213728 0.855429769 - 0.032213728 0.855429769 0.028842994 0.88596798 - 0.028842994 0.88596798 0.025360674 0.913078557 - 0.025360674 0.913078557 0.021780243 0.936656619 - 0.021780243 0.936656619 0.018115561 0.956610955 - 0.018115561 0.956610955 0.014380823 0.972864385 - 0.014380823 0.972864385 0.010590548 0.985354084 - 0.010590548 0.985354084 0.006759799 0.994031969 - 0.006759799 0.994031969 0.002908623 0.998866404 - 0.002908623 0.998866404 502 mat :

Manipulate the matrix:

tmp GaussLegendre.50 2 csort :

GaussLegendre.50 tmp 2 col tmp 1 col augment eval :

Answer for Jean

x f 4 x 2^1 + / :

a 0 :

b 1 :

I π :

Setup

1 f a b G Int.G c a b + 2 / : h b a - 2 / : X c h c UnitsOf * G 1 col * + eval : 13 mat N G rows : n Clear 12 mat h G n 2 el X n el f * n 1 N sum * 31 line :

x f x a b int I - 5.9656 1015 -^*

With Gauss Laguerre

https://keisan.casio.com/exec/system/1280801905

x f a b GaussLaguerre.50 Int.G I - 2.502 1015 -^*

With Gauss Legendre

https://pomax.github.io/bezierinfo/legendre-gauss.html

x f a b GaussLegendre.50 Int.G I - 6.218 109 -^*

Alvaro