Tài liệu Special Functions part 6 pdf

... (6. 5.8). y=x*x; ans1 = -2957821389.0+y*(7 062 834 065 .0+y*(-512359803 .6 +y*(10879881.29+y*(- 863 27.92757+y*228. 462 2733)))); ans2=400 765 44 269 .0+y*(745249 964 .8+y*(7189 466 .438 +y*(47447. 264 70+y*(2 26. 1030244+y*1.0)))); ans=(ans1/ans2)+0 .63 661 9772*bessj0(x)*log(x); } ... America). z=8.0/x; y=z*z; xx=x-0.785398 164 ; ans1=1.0+y*(-0.109 862 862 7e-2+y*(0.2734510407e-4 +y*(-0.20...

Ngày tải lên: 21/01/2014, 18:20

... 199–2 16; 19 76, op. cit. , vol. 80B, pp. 291–311. Amos D.E. 1980, ACM Transactions on Mathematical Software , vol. 6, pp. 365 –377 [1]; also vol. 6, pp. 420–428. Abramowitz, M., and Stegun, I.A. 1 964 , Handbook ... expint"); else { if (n == 0) ans=exp(-x)/x; Special case. else { if (x == 0.0) ans=1.0/nm1; Another special case. else { 224 Chapter 6. Special Functions Sample...

Ngày tải lên: 21/01/2014, 18:20

... fit. y=x*x/4.0; ans=(-log(x/2.0)*bessi0(x))+(-0.57721 566 +y*(0.42278420 +y*(0.23 069 7 56+ y*(0.3488590e-1+y*(0. 262 698e-2 +y*(0.10750e-3+y*0.74e-5)))))); } else { y=2.0/x; ans=(exp(-x)/sqrt(x))*(1.25331414+y*(-0.7832358e-1 +y*(0.2189 568 e-1+y*(-0.1 062 446e-1+y*(0.587872e-2 +y*(-0.251540e-2+y*0.53208e-3)))))); } return ... fit. y=x*x/4.0; ans=(log(x/2.0)*bessi1(x))+(1.0/x)*(1.0+y*(0.1544314...

Ngày tải lên: 21/01/2014, 18:20

... ∼ 1 2 + 1 πx sin  π 2 x 2  ,S(x)∼ 1 2 − 1 πx cos  π 2 x 2  (6. 9.5) Thus the precision of the routine frenel may be limited by the precision of the library routines for sine and cosine for large x. 2 56 Chapter 6. Special Functions Sample ... t t dt (6. 9 .6) Here γ ≈ 0.5772 is Euler’s constant. We only need a way to calculate the functions for x>0, because Si(−x)=−Si(x), Ci...

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Ngày tải lên: 14/12/2013, 16:16

... trade@cup.cam.ac.uk (outside North America). Chapter 6. Special Functions 6. 0 Introduction There is nothing particularly special about a special function, except that some person in authority ... the moniker. Special functions are sometimes called higher transcendental functions( higher than what?) or functionsof mathematicalphysics (but they occur in other fields also) or fun...

Ngày tải lên: 24/12/2013, 12:16

... good enough. double x,y,tmp,ser; static double cof [6] ={ 76. 180091729471 46, - 86. 5053203294 167 7, 24.01409824083091,-1.231739572450155, 0.120 865 0973 866 179e-2,-0.5395239384953e-5}; int j; y=x=xx; tmp=x+5.5; tmp ... for the complex gamma function, everywhere in the half complex plane Re z>0. 214 Chapter 6. Special Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SC...

Ngày tải lên: 21/01/2014, 18:20

... +5−a− ···  (x>0) (6. 2.7) It turns out that (6. 2.5) converges rapidly for x less than about a +1, while (6. 2 .6) or (6. 2.7) converges rapidly for x greater than about a+1. In these respective 218 Chapter 6. Special ... 10 −7 . { float t,z,ans; z=fabs(x); t=1.0/(1.0+0.5*z); ans=t*exp(-z*z-1. 265 51223+t*(1.00002 368 +t*(0.374091 96+ t*(0.0 967 8418+ t*(-0.1 862 88 06+ t*(0.278 868...

Ngày tải lên: 21/01/2014, 18:20

... 19 76, Journal of Research of the National Bureau of Standards , vol. 80B, pp. 291–311; 1981, op. cit. , vol. 86, pp. 66 1 68 6. Abramowitz, M., and Stegun, I.A. 1 964 , Handbook of Mathematical Functions , ... to x/h,andx 0 ≡n 0 h,x  ≡x−x 0 ,andn  ≡n−n 0 ,sothat F(x)≈ 1 √ π N  n  =−N n  odd e −(x  −n  h) 2 n  + n 0 , (6. 10.4) 260 Chapter 6. Special Functions Sample page f...

Ngày tải lên: 21/01/2014, 18:20