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History of Central finite difference coefficients

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2026-09-17 13:51 zeta3 table-repair@2.0+dc0f96a0 clarify Lagrange notation and accuracy order current reviewed
2026-09-17 13:39 zeta3 table-build@2.0+395f185d shorten definition after audit
2026-09-17 13:38 zeta3 with codex-c table-build@2.0+395f185d central finite difference coefficients
2026-09-17 13:34 zeta3 table-build@2.0+395f185d draft central finite difference coefficients

What changed between 2026-09-17 13:34 and 2026-09-17 13:38

from line 87 (907 lines, 904 more than before) @@ -87,3 +87,907 @@ 
 Display properties:   number-header: $a_{m,r,j}$-Numbers: []+Numbers:+- params:+    m: '1'+    r: '1'+    j: '-1'+  number: -1/2+  comment: 'Derivative order $m=1$, 2-order central formula: $\tfrac{1}{2}(-1,0,1)$.'+- params:+    m: '1'+    r: '1'+    j: '1'+  number: 1/2+- params:+    m: '1'+    r: '2'+    j: '-2'+  number: 1/12+  comment: 'Derivative order $m=1$, 4-order central formula: $\tfrac{1}{12}(1,-8,0,8,-1)$.'+- params:+    m: '1'+    r: '2'+    j: '-1'+  number: -2/3+- params:+    m: '1'+    r: '2'+    j: '1'+  number: 2/3+- params:+    m: '1'+    r: '2'+    j: '2'+  number: -1/12+- params:+    m: '1'+    r: '3'+    j: '-3'+  number: -1/60+  comment: 'Derivative order $m=1$, 6-order central formula: $\tfrac{1}{60}(-1,9,-45,0,45,-9,1)$.'+- params:+    m: '1'+    r: '3'+    j: '-2'+  number: 3/20+- params:+    m: '1'+    r: '3'+    j: '-1'+  number: -3/4+- params:+    m: '1'+    r: '3'+    j: '1'+  number: 3/4+- params:+    m: '1'+    r: '3'+    j: '2'+  number: -3/20+- params:+    m: '1'+    r: '3'+    j: '3'+  number: 1/60+- params:+    m: '1'+    r: '4'+    j: '-4'+  number: 1/280+  comment: 'Derivative order $m=1$, 8-order central formula: $\tfrac{1}{840}(3,-32,168,-672,0,672,-168,32,-3)$.'+- params:+    m: '1'+    r: '4'+    j: '-3'+  number: -4/105+- params:+    m: '1'+    r: '4'+    j: '-2'+  number: 1/5+- params:+    m: '1'+    r: '4'+    j: '-1'+  number: -4/5+- params:+    m: '1'+    r: '4'+    j: '1'+  number: 4/5+- params:+    m: '1'+    r: '4'+    j: '2'+  number: -1/5+- params:+    m: '1'+    r: '4'+    j: '3'+  number: 4/105+- params:+    m: '1'+    r: '4'+    j: '4'+  number: -1/280+- params:+    m: '1'+    r: '5'+    j: '-5'+  number: -1/1260+  comment: 'Derivative order $m=1$, 10-order central formula: $\tfrac{1}{2520}(-2,25,-150,600,-2100,0,2100,-600,150,-25,2)$.'+- params:+    m: '1'+    r: '5'+    j: '-4'+  number: 5/504+- params:+    m: '1'+    r: '5'+    j: '-3'+  number: -5/84+- params:+    m: '1'+    r: '5'+    j: '-2'+  number: 5/21+- params:+    m: '1'+    r: '5'+    j: '-1'+  number: -5/6+- params:+    m: '1'+    r: '5'+    j: '1'+  number: 5/6+- params:+    m: '1'+    r: '5'+    j: '2'+  number: -5/21+- params:+    m: '1'+    r: '5'+    j: '3'+  number: 5/84+- params:+    m: '1'+    r: '5'+    j: '4'+  number: -5/504+- params:+    m: '1'+    r: '5'+    j: '5'+  number: 1/1260+- params:+    m: '2'+    r: '1'+    j: '-1'+  number: '1'+  comment: 'Derivative order $m=2$, 2-order central formula: $1(1,-2,1)$.'+- params:+    m: '2'+    r: '1'+    j: '0'+  number: '-2'+- params:+    m: '2'+    r: '1'+    j: '1'+  number: '1'+- params:+    m: '2'+    r: '2'+    j: '-2'+  number: -1/12+  comment: 'Derivative order $m=2$, 4-order central formula: $\tfrac{1}{12}(-1,16,-30,16,-1)$.'+- params:+    m: '2'+    r: '2'+    j: '-1'+  number: 4/3+- params:+    m: '2'+    r: '2'+    j: '0'+  number: -5/2+- params:+    m: '2'+    r: '2'+    j: '1'+  number: 4/3+- params:+    m: '2'+    r: '2'+    j: '2'+  number: -1/12+- params:+    m: '2'+    r: '3'+    j: '-3'+  number: 1/90+  comment: 'Derivative order $m=2$, 6-order central formula: $\tfrac{1}{180}(2,-27,270,-490,270,-27,2)$.'+- params:+    m: '2'+    r: '3'+    j: '-2'+  number: -3/20+- params:+    m: '2'+    r: '3'+    j: '-1'+  number: 3/2+- params:+    m: '2'+    r: '3'+    j: '0'+  number: -49/18+- params:+    m: '2'+    r: '3'+    j: '1'+  number: 3/2+- params:+    m: '2'+    r: '3'+    j: '2'+  number: -3/20+- params:+    m: '2'+    r: '3'+    j: '3'+  number: 1/90+- params:+    m: '2'+    r: '4'+    j: '-4'+  number: -1/560+  comment: 'Derivative order $m=2$, 8-order central formula: $\tfrac{1}{5040}(-9,128,-1008,8064,-14350,8064,-1008,128,-9)$.'+- params:+    m: '2'+    r: '4'+    j: '-3'+  number: 8/315+- params:+    m: '2'+    r: '4'+    j: '-2'+  number: -1/5+- params:+    m: '2'+    r: '4'+    j: '-1'+  number: 8/5+- params:+    m: '2'+    r: '4'+    j: '0'+  number: -205/72+- params:+    m: '2'+    r: '4'+    j: '1'+  number: 8/5+- params:+    m: '2'+    r: '4'+    j: '2'+  number: -1/5+- params:+    m: '2'+    r: '4'+    j: '3'+  number: 8/315+- params:+    m: '2'+    r: '4'+    j: '4'+  number: -1/560+- params:+    m: '2'+    r: '5'+    j: '-5'+  number: 1/3150+  comment: 'Derivative order $m=2$, 10-order central formula: $\tfrac{1}{25200}(8,-125,1000,-6000,42000,-73766,42000,-6000,1000,-125,8)$.'+- params:+    m: '2'+    r: '5'+    j: '-4'+  number: -5/1008+- params:+    m: '2'+    r: '5'+    j: '-3'+  number: 5/126+- params:+    m: '2'+    r: '5'+    j: '-2'+  number: -5/21+- params:+    m: '2'+    r: '5'+    j: '-1'+  number: 5/3+- params:+    m: '2'+    r: '5'+    j: '0'+  number: -5269/1800+- params:+    m: '2'+    r: '5'+    j: '1'+  number: 5/3+- params:+    m: '2'+    r: '5'+    j: '2'+  number: -5/21+- params:+    m: '2'+    r: '5'+    j: '3'+  number: 5/126+- params:+    m: '2'+    r: '5'+    j: '4'+  number: -5/1008+- params:+    m: '2'+    r: '5'+    j: '5'+  number: 1/3150+- params:+    m: '3'+    r: '2'+    j: '-2'+  number: -1/2+  comment: 'Derivative order $m=3$, 2-order central formula: $\tfrac{1}{2}(-1,2,0,-2,1)$.'+- params:+    m: '3'+    r: '2'+    j: '-1'+  number: '1'+- params:+    m: '3'+    r: '2'+    j: '1'+  number: '-1'+- params:+    m: '3'+    r: '2'+    j: '2'+  number: 1/2+- params:+    m: '3'+    r: '3'+    j: '-3'+  number: 1/8+  comment: 'Derivative order $m=3$, 4-order central formula: $\tfrac{1}{8}(1,-8,13,0,-13,8,-1)$.'+- params:+    m: '3'+    r: '3'+    j: '-2'+  number: '-1'+- params:+    m: '3'+    r: '3'+    j: '-1'+  number: 13/8+- params:+    m: '3'+    r: '3'+    j: '1'+  number: -13/8+- params:+    m: '3'+    r: '3'+    j: '2'+  number: '1'+- params:+    m: '3'+    r: '3'+    j: '3'+  number: -1/8+- params:+    m: '3'+    r: '4'+    j: '-4'+  number: -7/240+  comment: 'Derivative order $m=3$, 6-order central formula: $\tfrac{1}{240}(-7,72,-338,488,0,-488,338,-72,7)$.'+- params:+    m: '3'+    r: '4'+    j: '-3'+  number: 3/10+- params:+    m: '3'+    r: '4'+    j: '-2'+  number: -169/120+- params:+    m: '3'+    r: '4'+    j: '-1'+  number: 61/30+- params:+    m: '3'+    r: '4'+    j: '1'+  number: -61/30+- params:+    m: '3'+    r: '4'+    j: '2'+  number: 169/120+- params:+    m: '3'+    r: '4'+    j: '3'+  number: -3/10+- params:+    m: '3'+    r: '4'+    j: '4'+  number: 7/240+- params:+    m: '3'+    r: '5'+    j: '-5'+  number: 41/6048+  comment: 'Derivative order $m=3$, 8-order central formula: $\tfrac{1}{30240}(205,-2522,14607,-52428,70098,0,-70098,52428,-14607,2522,-205)$.'+- params:+    m: '3'+    r: '5'+    j: '-4'+  number: -1261/15120+- params:+    m: '3'+    r: '5'+    j: '-3'+  number: 541/1120+- params:+    m: '3'+    r: '5'+    j: '-2'+  number: -4369/2520+- params:+    m: '3'+    r: '5'+    j: '-1'+  number: 1669/720+- params:+    m: '3'+    r: '5'+    j: '1'+  number: -1669/720+- params:+    m: '3'+    r: '5'+    j: '2'+  number: 4369/2520+- params:+    m: '3'+    r: '5'+    j: '3'+  number: -541/1120+- params:+    m: '3'+    r: '5'+    j: '4'+  number: 1261/15120+- params:+    m: '3'+    r: '5'+    j: '5'+  number: -41/6048+- params:+    m: '4'+    r: '2'+    j: '-2'+  number: '1'+  comment: 'Derivative order $m=4$, 2-order central formula: $1(1,-4,6,-4,1)$.'+- params:+    m: '4'+    r: '2'+    j: '-1'+  number: '-4'+- params:+    m: '4'+    r: '2'+    j: '0'+  number: '6'+- params:+    m: '4'+    r: '2'+    j: '1'+  number: '-4'+- params:+    m: '4'+    r: '2'+    j: '2'+  number: '1'+- params:+    m: '4'+    r: '3'+    j: '-3'+  number: -1/6+  comment: 'Derivative order $m=4$, 4-order central formula: $\tfrac{1}{6}(-1,12,-39,56,-39,12,-1)$.'+- params:+    m: '4'+    r: '3'+    j: '-2'+  number: '2'+- params:+    m: '4'+    r: '3'+    j: '-1'+  number: -13/2+- params:+    m: '4'+    r: '3'+    j: '0'+  number: 28/3+- params:+    m: '4'+    r: '3'+    j: '1'+  number: -13/2+- params:+    m: '4'+    r: '3'+    j: '2'+  number: '2'+- params:+    m: '4'+    r: '3'+    j: '3'+  number: -1/6+- params:+    m: '4'+    r: '4'+    j: '-4'+  number: 7/240+  comment: 'Derivative order $m=4$, 6-order central formula: $\tfrac{1}{240}(7,-96,676,-1952,2730,-1952,676,-96,7)$.'+- params:+    m: '4'+    r: '4'+    j: '-3'+  number: -2/5+- params:+    m: '4'+    r: '4'+    j: '-2'+  number: 169/60+- params:+    m: '4'+    r: '4'+    j: '-1'+  number: -122/15+- params:+    m: '4'+    r: '4'+    j: '0'+  number: 91/8+- params:+    m: '4'+    r: '4'+    j: '1'+  number: -122/15+- params:+    m: '4'+    r: '4'+    j: '2'+  number: 169/60+- params:+    m: '4'+    r: '4'+    j: '3'+  number: -2/5+- params:+    m: '4'+    r: '4'+    j: '4'+  number: 7/240+- params:+    m: '4'+    r: '5'+    j: '-5'+  number: -41/7560+  comment: 'Derivative order $m=4$, 8-order central formula: $\tfrac{1}{15120}(-82,1261,-9738,52428,-140196,192654,-140196,52428,-9738,1261,-82)$.'+- params:+    m: '4'+    r: '5'+    j: '-4'+  number: 1261/15120+- params:+    m: '4'+    r: '5'+    j: '-3'+  number: -541/840+- params:+    m: '4'+    r: '5'+    j: '-2'+  number: 4369/1260+- params:+    m: '4'+    r: '5'+    j: '-1'+  number: -1669/180+- params:+    m: '4'+    r: '5'+    j: '0'+  number: 1529/120+- params:+    m: '4'+    r: '5'+    j: '1'+  number: -1669/180+- params:+    m: '4'+    r: '5'+    j: '2'+  number: 4369/1260+- params:+    m: '4'+    r: '5'+    j: '3'+  number: -541/840+- params:+    m: '4'+    r: '5'+    j: '4'+  number: 1261/15120+- params:+    m: '4'+    r: '5'+    j: '5'+  number: -41/7560+- params:+    m: '5'+    r: '3'+    j: '-3'+  number: -1/2+  comment: 'Derivative order $m=5$, 2-order central formula: $\tfrac{1}{2}(-1,4,-5,0,5,-4,1)$.'+- params:+    m: '5'+    r: '3'+    j: '-2'+  number: '2'+- params:+    m: '5'+    r: '3'+    j: '-1'+  number: -5/2+- params:+    m: '5'+    r: '3'+    j: '1'+  number: 5/2+- params:+    m: '5'+    r: '3'+    j: '2'+  number: '-2'+- params:+    m: '5'+    r: '3'+    j: '3'+  number: 1/2+- params:+    m: '5'+    r: '4'+    j: '-4'+  number: 1/6+  comment: 'Derivative order $m=5$, 4-order central formula: $\tfrac{1}{6}(1,-9,26,-29,0,29,-26,9,-1)$.'+- params:+    m: '5'+    r: '4'+    j: '-3'+  number: -3/2+- params:+    m: '5'+    r: '4'+    j: '-2'+  number: 13/3+- params:+    m: '5'+    r: '4'+    j: '-1'+  number: -29/6+- params:+    m: '5'+    r: '4'+    j: '1'+  number: 29/6+- params:+    m: '5'+    r: '4'+    j: '2'+  number: -13/3+- params:+    m: '5'+    r: '4'+    j: '3'+  number: 3/2+- params:+    m: '5'+    r: '4'+    j: '4'+  number: -1/6+- params:+    m: '5'+    r: '5'+    j: '-5'+  number: -13/288+  comment: 'Derivative order $m=5$, 6-order central formula: $\tfrac{1}{288}(-13,152,-783,1872,-1938,0,1938,-1872,783,-152,13)$.'+- params:+    m: '5'+    r: '5'+    j: '-4'+  number: 19/36+- params:+    m: '5'+    r: '5'+    j: '-3'+  number: -87/32+- params:+    m: '5'+    r: '5'+    j: '-2'+  number: 13/2+- params:+    m: '5'+    r: '5'+    j: '-1'+  number: -323/48+- params:+    m: '5'+    r: '5'+    j: '1'+  number: 323/48+- params:+    m: '5'+    r: '5'+    j: '2'+  number: -13/2+- params:+    m: '5'+    r: '5'+    j: '3'+  number: 87/32+- params:+    m: '5'+    r: '5'+    j: '4'+  number: -19/36+- params:+    m: '5'+    r: '5'+    j: '5'+  number: 13/288+- params:+    m: '6'+    r: '3'+    j: '-3'+  number: '1'+  comment: 'Derivative order $m=6$, 2-order central formula: $1(1,-6,15,-20,15,-6,1)$.'+- params:+    m: '6'+    r: '3'+    j: '-2'+  number: '-6'+- params:+    m: '6'+    r: '3'+    j: '-1'+  number: '15'+- params:+    m: '6'+    r: '3'+    j: '0'+  number: '-20'+- params:+    m: '6'+    r: '3'+    j: '1'+  number: '15'+- params:+    m: '6'+    r: '3'+    j: '2'+  number: '-6'+- params:+    m: '6'+    r: '3'+    j: '3'+  number: '1'+- params:+    m: '6'+    r: '4'+    j: '-4'+  number: -1/4+  comment: 'Derivative order $m=6$, 4-order central formula: $\tfrac{1}{4}(-1,12,-52,116,-150,116,-52,12,-1)$.'+- params:+    m: '6'+    r: '4'+    j: '-3'+  number: '3'+- params:+    m: '6'+    r: '4'+    j: '-2'+  number: '-13'+- params:+    m: '6'+    r: '4'+    j: '-1'+  number: '29'+- params:+    m: '6'+    r: '4'+    j: '0'+  number: -75/2+- params:+    m: '6'+    r: '4'+    j: '1'+  number: '29'+- params:+    m: '6'+    r: '4'+    j: '2'+  number: '-13'+- params:+    m: '6'+    r: '4'+    j: '3'+  number: '3'+- params:+    m: '6'+    r: '4'+    j: '4'+  number: -1/4+- params:+    m: '6'+    r: '5'+    j: '-5'+  number: 13/240+  comment: 'Derivative order $m=6$, 6-order central formula: $\tfrac{1}{240}(13,-190,1305,-4680,9690,-12276,9690,-4680,1305,-190,13)$.'+- params:+    m: '6'+    r: '5'+    j: '-4'+  number: -19/24+- params:+    m: '6'+    r: '5'+    j: '-3'+  number: 87/16+- params:+    m: '6'+    r: '5'+    j: '-2'+  number: -39/2+- params:+    m: '6'+    r: '5'+    j: '-1'+  number: 323/8+- params:+    m: '6'+    r: '5'+    j: '0'+  number: -1023/20+- params:+    m: '6'+    r: '5'+    j: '1'+  number: 323/8+- params:+    m: '6'+    r: '5'+    j: '2'+  number: -39/2+- params:+    m: '6'+    r: '5'+    j: '3'+  number: 87/16+- params:+    m: '6'+    r: '5'+    j: '4'+  number: -19/24+- params:+    m: '6'+    r: '5'+    j: '5'+  number: 13/240

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