p⋍(１/2)±11⒤[√(1-s)-(q/11)]⋍(h/2)Cosθ (橋本p132)

p⋍(１/2)±11⒤[√(1-s)-(q/11)] ⋍(h/2)Cosθ (橋本p132)
s (1-s) √(1-s) -(q/11) σ x11 文献値
-2 3 1.732050808 0.454545455 1.277505353 14.05255888 14.13472
-4 5 2.236067977 0.363636364 1.872431614 20.59674775 21.02203
-6 7 2.645751311 0.363636364 2.282114947 25.10326442 25.01085
-8 9 3 2.75 30.25 ( 30.42487 )
-10 11 3.31662479 0.363636364 2.952988427 32.48287269 ( 32.93506 )
-12 13 3.605551275 0.636363636 2.969187639 32.66106403 ( 32.93506 )
-14 15 3.872983346 0.454545455 3.418437892 37.60281681 37.58617
-16 17 4.123105626 0.454545455 3.668560171 40.35416188 40.91871
-18 19 4.358898944 0.454545455 3.904353489 42.94788838 43.32707
-20 21 4.582575695 0.181818182 4.400757513 48.40833264 48.00515
-22 23 4.795831523 0.27272727 4.523104253 49.75414679 49.77383
-24 25 5 0.181818182 4.818181818 53 52.97
-26 27 5.196152423 0.090909091 5.105243332 56.15767665 56.446
-28 29 5.385164807 5.385164807 59.23681288 59.347
-30 31 5.567764363 0.090909091 5.476855272 60.24540799 60.831
-32 33 5.744562647 5.744562647 63.19018911 ( 65.112 )
-34 35 5.916079783 5.916079783 65.07687761 ( 65.112 )
-36 37 6.08276253 0.181818182 5.900944348 64.91038783 ( 65.112 )
-38 39 6.244997998 0.363636364 5.881361635 64.69497798 ( 65.112 )
-40 41 6.403124237 0.454545455 5.948578783 65.43436661 ( 65.112 )
-42 43 6.557438524 0.090909091 6.466529433 71.13182377
-44 45 6.708203932 0.090909091 6.617294842 72.79024326
-46 47 6.8556546 0.090909091 6.764745509 74.4122006
-48 49 7 0.090909091 6.909090909 76 75.8
-50 51 7.141428429 0.090909091 7.050519338 77.55571271

∴Γs+1⋍(s-1)Γs

②Γ⋍k＾2-A⋍-A/k^2 ∴Γs+1⋍(s-1)Γs
Γ(s.5) s Γ⋆/Γ⋆⋆ L⋍ℓ(ℓ+1) ⋍3+2ｎ
1.77245 0.5
0.886227 1.5 0.500001128 0.750001693
1.32934 2.5 1.499999436 3.74999859 2.999996897
3.32335 3.5 2.5 8.75 5.00000141
11.6317 4.5 3.499992477 15.74996615 6.999966149
52.3428 5.5 4.500012896 24.75007093 9.000104778
287.885 6.5 5.499992358 35.74995033 10.9998794
1871.25 7.5 6.499991316 48.74993487 12.99998454
14034.4 8.5 7.50001336 63.75011356 15.00017869
119292 9.5 8.499971499 80.74972924 16.99961568
ｓ -(1-s)
　Γs+1/Γs ⋍-(1-s) ∴Γs+1⋍(s-1)Γs
Γ(s.75) s Γ⋆/Γ⋆⋆ L⋍ℓ(ℓ+1) ⋍3.5+2ｎ
1.22542 0.75
0.919063 1.75 0.749998368 1.312497144
1.60836 2.75 1.749999728 4.812499252 3.500002108
4.42299 3.75 2.75 10.3125 5.500000748
16.5862 4.75 3.749997174 17.81248658 7.499986576
78.7845 5.75 4.750003015 27.31251733 9.500030758
453.011 6.75 5.750001587 38.81251071 11.49999338
3057.82 6.75 6.749990618 45.56243667 6.749925964
23698.1 7.75 7.749998365 60.06248733 14.50005065
207359 8.75 8.750026373 76.56273077 16.50024344

∴Γs+1⋍(s-1)Γs

②Γ⋍k＾2-A⋍-A/k^2 ∴Γs+1⋍(s-1)Γs
Γ(s.25) s Γ⋆/Γ⋆⋆ L⋍ℓ(ℓ+1) ⋍2.5+2ｎ
3.62561 0.25
0.906402 1.25 0.249999862 0.312499828
1.133 2.25 1.249997242 2.812493794 2.499993967
2.54926 3.25 2.250008826 7.312528685 4.500034891
8.28509 4.25 3.249998039 13.81249166 6.499962979
35.2116 5.25 4.249996077 22.31247941 8.499987742
184.861 6.25 5.25000284 32.81251775 10.50003834
1155.38 7.25 6.249993238 45.31245098 12.49993323
8376.51 8.25 7.250004328 59.8125357 14.50008473
69106.2 9.25 8.249999105 76.31249172 16.49995602
ｓ -(1-s)
　Γs+1/Γs ⋍-(1-s) ∴Γs+1⋍(s-1)Γs

連分数 k^2+A (k=1.133)

連分数　k^2+A　(k=1.133)
②Γ⋍k＾2-A⋍-A/k^2
Γ(s) Γ/Γ Γ(s.25) Γ⋆/Γ⋆⋆ Γ(s.5) Γ⋆/Γ⋆⋆ Γ(s.75) Γ⋆/Γ⋆⋆
1 3.62561 1.77245 1.22542
1 1 0.906402 0.249999862 0.886227 0.500001128 0.919063 0.749998368
2 2 1.133 1.249997242 1.32934 1.499999436 1.60836 1.749999728
6 3 2.54926 2.250008826 3.32335 2.5 4.42299 2.75
24 4 8.28509 3.249998039 11.6317 3.499992477 16.5862 3.749997174
120 5 35.2116 4.249996077 52.3428 4.500012896 78.7845 4.750003015
720 6 184.861 5.25000284 287.885 5.499992358 453.011 5.750001587
5040 7 1155.38 6.249993238 1871.25 6.499991316 3057.82 6.749990618
40320 8 8376.51 7.250004328 14034.4 7.50001336 23698.1 7.749998365
9 69106.2 8.249999105 119292 8.499971499 207359 8.750026373

連分数 k^2+A (k=1.133)

①φ⋍k^2+A ②Γ⋍k＾2-A⋍-A/k^2 ③p⋍11(k^2+A)
k^2 +A(⋍1/3) Γ(s.25) Γ⋆/Γ⋆⋆
3.62561
1.133 1.466333333 0.906402 0.249999862 文献値 文/11 ⋍(1.133)^2
1.283689 1.617022333 φ 1.133 1.249997242 14.13472 1.284974545 ⋍√ 1.133567177
1.454419637 1.950355667 2.54926 2.250008826 21.02203 1.911093636 ⋆/⋆ 1.487261863
1.647857449 2.283689 8.28509 3.249998039 25.01085 2.273713636 ⋆/⋆ 1.189744758
1.867022489 2.617022333 φ+1 35.2116 4.249996077 30.42487 2.765897273 ⋆/⋆ 1.216466853
2.11533648 2.950355667 184.861 5.25000284 32.93506 2.994096364 ⋆/⋆ 1.082504543
2.396676232 3.283689 1155.38 6.249993238 37.58617 3.416924545 ⋆/⋆ 1.141220632
2.715434171 3.617022333 φ+2 8376.51 7.250004328 40.91871 3.719882727 ⋆/⋆ 1.088663995
3.076586916 3.950355667 69106.2 8.249999105 43.32707 3.938824545 ⋆/⋆ 1.058857183
3.485772976 4.283689 48.00515 4.364104545 ⋆/⋆ 1.107971298
3.949380782 4.617022333 φ+3 49.77383 4.524893636 ⋆/⋆ 1.036843547
4.474648426 4.950355667 52.97 4.815454545 ⋆/⋆ 1.064213865
5.069776666 5.283689 56.446 5.131454545 ⋆/⋆ 1.06562205
5.744056963 5.617022333 φ+4 59.347 5.395181818 ⋆/⋆ 1.051394253
6.508016539 5.950355667 60.831 5.530090909 ⋆/⋆ 1.025005476
7.373582739 6.283689 65.112 5.919272727 ⋆/⋆ 1.070375302
75.8 6.890909091 ⋆/⋆ 1.16414793