History of Backward differentiation formula coefficients

       \    out.update({'alpha_%d' % j: alpha[j] for j in range(s + 1)})\n    return\       \ out\n\nbdf_coefficients(3)"-Numbers: []+Numbers:+- params:+    s: '1'+    normalisation: alpha-s-one+    coefficient: alpha_0+  number: '-1'+  param-latex: $\alpha_{s,0}$+  comment: 'Backward Euler method, from newest to oldest: $\tfrac{1}{1}(1,-1)$, with+    $\beta_1=1$.'+- params:+    s: '1'+    normalisation: alpha-s-one+    coefficient: beta+  number: '1'+  param-latex: $\beta_s$+- params:+    s: '1'+    normalisation: nabla+    coefficient: alpha_0+  number: '-1'+  param-latex: $\alpha_{s,0}$+- params:+    s: '1'+    normalisation: nabla+    coefficient: alpha_1+  number: '1'+  param-latex: $\alpha_{s,1}$+- params:+    s: '2'+    normalisation: alpha-s-one+    coefficient: alpha_0+  number: 1/3+  param-latex: $\alpha_{s,0}$+  comment: '2-step BDF formula, from newest to oldest: $\tfrac{1}{3}(3,-4,1)$, with+    $\beta_2=\tfrac{2}{3}$.'+- params:+    s: '2'+    normalisation: alpha-s-one+    coefficient: alpha_1+  number: -4/3+  param-latex: $\alpha_{s,1}$+- params:+    s: '2'+    normalisation: alpha-s-one+    coefficient: beta+  number: 2/3+  param-latex: $\beta_s$+- params:+    s: '2'+    normalisation: nabla+    coefficient: alpha_0+  number: 1/2+  param-latex: $\alpha_{s,0}$+- params:+    s: '2'+    normalisation: nabla+    coefficient: alpha_1+  number: '-2'+  param-latex: $\alpha_{s,1}$+- params:+    s: '2'+    normalisation: nabla+    coefficient: alpha_2+  number: 3/2+  param-latex: $\alpha_{s,2}$+- params:+    s: '3'+    normalisation: alpha-s-one+    coefficient: alpha_0+  number: -2/11+  param-latex: $\alpha_{s,0}$+  comment: '3-step BDF formula, from newest to oldest: $\tfrac{1}{11}(11,-18,9,-2)$,+    with $\beta_3=\tfrac{6}{11}$.'+- params:+    s: '3'+    normalisation: alpha-s-one+    coefficient: alpha_1+  number: 9/11+  param-latex: $\alpha_{s,1}$+- params:+    s: '3'+    normalisation: alpha-s-one+    coefficient: alpha_2+  number: -18/11+  param-latex: $\alpha_{s,2}$+- params:+    s: '3'+    normalisation: alpha-s-one+    coefficient: beta+  number: 6/11+  param-latex: $\beta_s$+- params:+    s: '3'+    normalisation: nabla+    coefficient: alpha_0+  number: -1/3+  param-latex: $\alpha_{s,0}$+- params:+    s: '3'+    normalisation: nabla+    coefficient: alpha_1+  number: 3/2+  param-latex: $\alpha_{s,1}$+- params:+    s: '3'+    normalisation: nabla+    coefficient: alpha_2+  number: '-3'+  param-latex: $\alpha_{s,2}$+- params:+    s: '3'+    normalisation: nabla+    coefficient: alpha_3+  number: 11/6+  param-latex: $\alpha_{s,3}$+- params:+    s: '4'+    normalisation: alpha-s-one+    coefficient: alpha_0+  number: 3/25+  param-latex: $\alpha_{s,0}$+  comment: '4-step BDF formula, from newest to oldest: $\tfrac{1}{25}(25,-48,36,-16,3)$,+    with $\beta_4=\tfrac{12}{25}$.'+- params:+    s: '4'+    normalisation: alpha-s-one+    coefficient: alpha_1+  number: -16/25+  param-latex: $\alpha_{s,1}$+- params:+    s: '4'+    normalisation: alpha-s-one+    coefficient: alpha_2+  number: 36/25+  param-latex: $\alpha_{s,2}$+- params:+    s: '4'+    normalisation: alpha-s-one+    coefficient: alpha_3+  number: -48/25+  param-latex: $\alpha_{s,3}$+- params:+    s: '4'+    normalisation: alpha-s-one+    coefficient: beta+  number: 12/25+  param-latex: $\beta_s$+- params:+    s: '4'+    normalisation: nabla+    coefficient: alpha_0+  number: 1/4+  param-latex: $\alpha_{s,0}$+- params:+    s: '4'+    normalisation: nabla+    coefficient: alpha_1+  number: -4/3+  param-latex: $\alpha_{s,1}$+- params:+    s: '4'+    normalisation: nabla+    coefficient: alpha_2+  number: '3'+  param-latex: $\alpha_{s,2}$+- params:+    s: '4'+    normalisation: nabla+    coefficient: alpha_3+  number: '-4'+  param-latex: $\alpha_{s,3}$+- params:+    s: '4'+    normalisation: nabla+    coefficient: alpha_4+  number: 25/12+  param-latex: $\alpha_{s,4}$+- params:+    s: '5'+    normalisation: alpha-s-one+    coefficient: alpha_0+  number: -12/137+  param-latex: $\alpha_{s,0}$+  comment: '5-step BDF formula, from newest to oldest: $\tfrac{1}{137}(137,-300,300,-200,75,-12)$,+    with $\beta_5=\tfrac{60}{137}$.'+- params:+    s: '5'+    normalisation: alpha-s-one+    coefficient: alpha_1+  number: 75/137+  param-latex: $\alpha_{s,1}$+- params:+    s: '5'+    normalisation: alpha-s-one+    coefficient: alpha_2+  number: -200/137+  param-latex: $\alpha_{s,2}$+- params:+    s: '5'+    normalisation: alpha-s-one+    coefficient: alpha_3+  number: 300/137+  param-latex: $\alpha_{s,3}$+- params:+    s: '5'+    normalisation: alpha-s-one+    coefficient: alpha_4+  number: -300/137+  param-latex: $\alpha_{s,4}$+- params:+    s: '5'+    normalisation: alpha-s-one+    coefficient: beta+  number: 60/137+  param-latex: $\beta_s$+- params:+    s: '5'+    normalisation: nabla+    coefficient: alpha_0+  number: -1/5+  param-latex: $\alpha_{s,0}$+- params:+    s: '5'+    normalisation: nabla+    coefficient: alpha_1+  number: 5/4+  param-latex: $\alpha_{s,1}$+- params:+    s: '5'+    normalisation: nabla+    coefficient: alpha_2+  number: -10/3+  param-latex: $\alpha_{s,2}$+- params:+    s: '5'+    normalisation: nabla+    coefficient: alpha_3+  number: '5'+  param-latex: $\alpha_{s,3}$+- params:+    s: '5'+    normalisation: nabla+    coefficient: alpha_4+  number: '-5'+  param-latex: $\alpha_{s,4}$+- params:+    s: '5'+    normalisation: nabla+    coefficient: alpha_5+  number: 137/60+  param-latex: $\alpha_{s,5}$+- params:+    s: '6'+    normalisation: alpha-s-one+    coefficient: alpha_0+  number: 10/147+  param-latex: $\alpha_{s,0}$+  comment: '6-step BDF formula, from newest to oldest: $\tfrac{1}{147}(147,-360,450,-400,225,-72,10)$,+    with $\beta_6=\tfrac{20}{49}$.'+- params:+    s: '6'+    normalisation: alpha-s-one+    coefficient: alpha_1+  number: -24/49+  param-latex: $\alpha_{s,1}$+- params:+    s: '6'+    normalisation: alpha-s-one+    coefficient: alpha_2+  number: 75/49+  param-latex: $\alpha_{s,2}$+- params:+    s: '6'+    normalisation: alpha-s-one+    coefficient: alpha_3+  number: -400/147+  param-latex: $\alpha_{s,3}$+- params:+    s: '6'+    normalisation: alpha-s-one+    coefficient: alpha_4+  number: 150/49+  param-latex: $\alpha_{s,4}$+- params:+    s: '6'+    normalisation: alpha-s-one+    coefficient: alpha_5+  number: -120/49+  param-latex: $\alpha_{s,5}$+- params:+    s: '6'+    normalisation: alpha-s-one+    coefficient: beta+  number: 20/49+  param-latex: $\beta_s$+- params:+    s: '6'+    normalisation: nabla+    coefficient: alpha_0+  number: 1/6+  param-latex: $\alpha_{s,0}$+- params:+    s: '6'+    normalisation: nabla+    coefficient: alpha_1+  number: -6/5+  param-latex: $\alpha_{s,1}$+- params:+    s: '6'+    normalisation: nabla+    coefficient: alpha_2+  number: 15/4+  param-latex: $\alpha_{s,2}$+- params:+    s: '6'+    normalisation: nabla+    coefficient: alpha_3+  number: -20/3+  param-latex: $\alpha_{s,3}$+- params:+    s: '6'+    normalisation: nabla+    coefficient: alpha_4+  number: 15/2+  param-latex: $\alpha_{s,4}$+- params:+    s: '6'+    normalisation: nabla+    coefficient: alpha_5+  number: '-6'+  param-latex: $\alpha_{s,5}$+- params:+    s: '6'+    normalisation: nabla+    coefficient: alpha_6+  number: 49/20+  param-latex: $\alpha_{s,6}$