くだらねぇ問題はここへ書け ver.3.14(43桁略)3751
>>849
(1) 1/√(1-X^2) = 1 + (1/2)X^2 + (3!!/4!!)X^4 + … + {(2n-1)!!/(2n)!!}X^(2n) + …
arcsin(X) = ∫1/√(1-X^2) dX = X + (1/6)X^3 + {3!!/(4!!･5)}X^5 + … + {(2n-1)!!/[(2n)!!(2n+1)]}X^(2n+1) + …
(2) (1+Y)^(1/4) = 1 + (1/4)Y -(3/32)Y^2 -(7/128)Y^3 + … +(-1)^(n-1)･(1/4)(3/4)(7/4)…(n-5/4)(1/n!)X^n + …
= 1 + (1/4)Y -(3/32)Y^2 -(7/128)Y^3+ … +(-1)^(n-1)･{Γ(n-1/4)/4Γ(3/4)}(1/n!)X^n + …
これに Y=X^2 を代入汁
>>850
http://ja.wikipedia.org/wiki/%E3%82%AC%E3%83%B3%E3%83%9E%E9%96%A2%E6%95%B0
http://mathworld.wolfram.com/GammaFunction.html
http://functions.wolfram.com/GammaBetaErf/Gamma/
高木: ｢解析概論｣ 改訂第三版, 岩波 (1961) §68, p.248-258
(1) 1/√(1-X^2) = 1 + (1/2)X^2 + (3!!/4!!)X^4 + … + {(2n-1)!!/(2n)!!}X^(2n) + …
arcsin(X) = ∫1/√(1-X^2) dX = X + (1/6)X^3 + {3!!/(4!!･5)}X^5 + … + {(2n-1)!!/[(2n)!!(2n+1)]}X^(2n+1) + …
(2) (1+Y)^(1/4) = 1 + (1/4)Y -(3/32)Y^2 -(7/128)Y^3 + … +(-1)^(n-1)･(1/4)(3/4)(7/4)…(n-5/4)(1/n!)X^n + …
= 1 + (1/4)Y -(3/32)Y^2 -(7/128)Y^3+ … +(-1)^(n-1)･{Γ(n-1/4)/4Γ(3/4)}(1/n!)X^n + …
これに Y=X^2 を代入汁
>>850
http://ja.wikipedia.org/wiki/%E3%82%AC%E3%83%B3%E3%83%9E%E9%96%A2%E6%95%B0
http://mathworld.wolfram.com/GammaFunction.html
http://functions.wolfram.com/GammaBetaErf/Gamma/
高木: ｢解析概論｣ 改訂第三版, 岩波 (1961) §68, p.248-258
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