■ある無限級数(その116)

 1−x/a(a+1)+x^2/a(a+1)(a+2)(a+3)−x^3/a(a+1)(a+2)(a+3)(a+4)(a+5)+・・・

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 an=(a−1)!x^n/(a+2n−1)!

 an+1=(a−1)!x^n+1/(a+2n+1)!

 an+1/an=x/(a+2n)(a+2n+1)

 an+1/an=(n+1)/(n+a/2)(n+(a+1)/2)・x/4(n+1)

[1]a=1→0F1(1/2:−x^2/4)=cosx

[2]a=2→0F1(3/2:−x^2/4)=sinx/x

[3]a=3→1F2(1;3/2,2:−x^2/4)=?

[4]a=4→1F2(1;5/2,2:−x^2/4)=? (確認できず)

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