Tài liệu Special Functions part 7 pdf

... { y=3 .75 /ax; ans=(exp(ax)/sqrt(ax))*(0.39894228+y*(0.1328592e-1 +y*(0.225319e-2+y*(-0.1 575 65e-2+y*(0.916281e-2 +y*(-0.20 577 06e-1+y*(0.2635537e-1+y*(-0.16 476 33e-1 +y*0.392 377 e-2)))))))); } return ans; } #include <math.h> float ... precision. if ((ax=fabs(x)) < 3 .75 ) { Polynomial fit. y=x/3 .75 ; y*=y; ans=1.0+y*(3.5156229+y*(3.0899424+y*(1.20 674 92 +y*(0.265 973 2+y*(0.36...

Ngày tải lên: 21/01/2014, 18:20

... CDROMs visit website http://www.nr.com or call 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). where γ =0. 577 2156649 is Euler’s constant. We evaluate the ... 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 page fr...

Ngày tải lên: 21/01/2014, 18:20

... (6.5.8). y=x*x; ans1 = -29 578 21389.0+y* (70 62834065.0+y*(-512359803.6 +y*(10 879 881.29+y*(-863 27. 9 275 7+y*228.462 273 3)))); ans2=40 076 544269.0+y* (74 5249964.8+y* (71 89466.438 +y*( 474 47. 26 470 +y*(226.1030244+y*1.0)))); ans=(ans1/ans2)+0.63661 977 2*bessj0(x)*log(x); } ... fit. y=x*x; ans1= 575 68490 574 .0+y*(-13362590354.0+y*(651619640 .7 +y*(-11214424.18+y* (77 392.330 17+ y*...

Ngày tải lên: 21/01/2014, 18:20

... t t dt (6.9.6) Here γ ≈ 0. 577 2 is Euler’s constant. We only need a way to calculate the functions for x>0, because Si(−x)=−Si(x), Ci(−x)=Ci(x)−iπ (6.9 .7) Once again we can evaluate these functions by a ... error near a zero of Ci(x). #define EULER 0. 577 21566 Euler’s constant γ. #define MAXIT 100 Maximum number of iterations allowed. #define PIBY2 1. 570 7963 π/2. #define FPMIN 1....

Ngày tải lên: 26/01/2014, 15:20

... 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Chapter 6. Special Functions 6.0 Introduction There is nothing particularly special about a special ... the moniker. Special functions are sometimes called higher transcendental functions( higher than what?) or functionsof mathematicalphysics (but they occur in other fields also)...

Ngày tải lên: 24/12/2013, 12:16

... enough. double x,y,tmp,ser; static double cof[6]= {76 .18009 172 9 471 46,-86.50532032941 677 , 24.01409824083091,-1.23 173 9 572 450155, 0.1208650 973 866 179 e-2,-0.5395239384953e-5}; int j; y=x=xx; tmp=x+5.5; tmp ... 1955, Approximations for Digital Computers (Princeton: Princeton University Press). Luke, Y.L. 1 975 , Mathematical Functions and Their Approximations (New York: Academic Pr...

Ngày tải lên: 21/01/2014, 18:20

... than 1.2 × 10 7 . { float t,z,ans; z=fabs(x); t=1.0/(1.0+0.5*z); ans=t*exp(-z*z-1.26551223+t*(1.00002368+t*(0. 374 09196+t*(0.09 678 418+ t*(-0.18628806+t*(0. 278 868 07+ t*(-1.13520398+t*(1.488515 87+ t*(-0.82215223+t*0. 170 872 77) )))))))); return ... t,z,ans; z=fabs(x); t=1.0/(1.0+0.5*z); ans=t*exp(-z*z-1.26551223+t*(1.00002368+t*(0. 374 09196+t*(0.09 678 418+ t*(-0.18628806+t*(0. 278...

Ngày tải lên: 21/01/2014, 18:20

... order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). } if ... 1 976 , Journal of Research of the National Bureau of Standards , vol. 80B, pp. 291–311; 1981, op. cit. , vol. 86, pp. 661–686. Abramowitz, M., and Stegun, I.A. 1964, Handbook of Mathematical...

Ngày tải lên: 21/01/2014, 18:20

... 19 87, Mathematics of Computation , vol. 49, pp. 595–606 [4]; 1988, op. cit. , vol. 51, pp. 2 67 280 [5]; 1989, op. cit. , vol. 53, pp. 3 27 333 [6]; 1991, op. cit. , vol. 56, pp. 2 67 280. [7] Bulirsch, ... York), Chapter 17. [12] Mathews, J., and Walker, R.L. 1 970 , Mathematical Methods of Physics , 2nd ed. (Reading, MA: W.A. Benjamin/Addison-Wesley), pp. 78 79 . 6.12 Hypergeometric F...

Ngày tải lên: 21/01/2014, 18:20

... 19 87, Mathematics of Computation , vol. 49, pp. 595–606 [4]; 1988, op. cit. , vol. 51, pp. 2 67 280 [5]; 1989, op. cit. , vol. 53, pp. 3 27 333 [6]; 1991, op. cit. , vol. 56, pp. 2 67 280. [7] Bulirsch, ... York), Chapter 17. [12] Mathews, J., and Walker, R.L. 1 970 , Mathematical Methods of Physics , 2nd ed. (Reading, MA: W.A. Benjamin/Addison-Wesley), pp. 78 79 . 6.12 Hypergeometric F...

Ngày tải lên: 21/01/2014, 18:20