Calculation of Gamma Function.

Keyword

Gamma function,Euler's reflection formula,Gaussian integral,Approximation,Hastings,Factorial,Real number,Natural number.

Reference

・[1]：『数学ハンドブック』(I.N.ブロンシュテイン, K.A.セメンジャーエフ, G.グロッシェ).pp.121-122.
・[2]：『新版数値計算ハンドブック』(大野豊,磯田和男).pp.955-956.

Remarks

・Gamma function is calculated by approximation of Hastings.Therefore,it contains error.
・Γ(x+1)≈1+b1*x+b2*x^2+b3*x^3+b4*x^4+b5*x^5+b6*x^6+b7*x^7+b8*x^8.(Approximation of Hastings.Cited from Reference[2])
  b1=-0.577191652
  b2=0.988205891
  b3=-0.897056937
  b4=0.918206857
  b5=-0.756704078
  b6=0.482199394
  b7=-0.193527818
  b8=0.035868343
・Γ(1+x)=x*Γ(x).
・Γ(x)*Γ(-x)=-π/(x*sin(π*x)).(Cited from Reference[1])

History

・2009/07/01：Upload.