170111

Ruby

sinc function の積の積分(3)

Alois P. Heinz さんがこの先を求めてくれた。

# OEIS A280841のデータ
n_ary =
[1,1,1,1727,20652479,2059268143,24860948333867803,
 145905074443586569379,
 4567419249415312673370820607,
 1642142815363470261591271553081,
 4093745592094627817260334517735412136353665283]
# OEIS A280842のデータ
d_ary =
[2,2,2,3456,41472000,4147200000,50185433088000000,
 295090346557440000000,
 9251918060437194670080000000,
 3330690501757390081228800000000,
 8312243866372850396258184884618526720000000000]

n = n_ary.size
# In / Pi
p (1..n).map{|i| n_ary[i - 1].to_r / d_ary[i - 1]}
# In / Pi を小数で表示
p (1..n).map{|i| (n_ary[i - 1].to_r / d_ary[i - 1]).to_f}
# 1 / 2 と In / Pi との誤差
p (1..n).map{|i| 1r / 2 - n_ary[i - 1].to_r / d_ary[i - 1]}
# 1 / 2 と In / Pi との誤差を小数で表示
p (1..n).map{|i| (1r / 2 - n_ary[i - 1].to_r / d_ary[i - 1]).to_f}

出力結果
[(1/2), (1/2), (1/2), (1727/3456), (20652479/41472000), (2059268143/4147200000), (24860948333867803/50185433088000000), (145905074443586569379/295090346557440000000), (4567419249415312673370820607/9251918060437194670080000000), (1642142815363470261591271553081/3330690501757390081228800000000), (4093745592094627817260334517735412136353665283/8312243866372850396258184884618526720000000000)]
[0.5, 0.5, 0.5, 0.49971064814814814, 0.4979860869984568, 0.49654420886381173, 0.4953817632752956, 0.4944420451083303, 0.4936726870665218, 0.49303374615474405, 0.4924958480412081]
[(0/1), (0/1), (0/1), (1/3456), (83521/41472000), (14331857/4147200000), (231768210132197/50185433088000000), (1640098835133430621/295090346557440000000), (58539780803284661669179393/9251918060437194670080000000), (23202435515224779023128446919/3330690501757390081228800000000), (62376341091797380868757924573851223646334717/8312243866372850396258184884618526720000000000)]
[0.0, 0.0, 0.0, 0.00028935185185185184, 0.00201391300154321, 0.0034557911361882718, 0.004618236724704401, 0.005557954891669699, 0.006327312933478185, 0.006966253845255918, 0.007504151958791851]