Tài liệu Special Functions part 13 docx
Tài liệu Special Functions part 13 docx
... few steps are required to
integrate the equations. A half-dozen is typical.
272
Chapter 6. Special Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... READING:
Erd´elyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. 1953,
Higher Transcendental
Functions
, Vol. II, (New York: McGraw-Hill). [1]
Gradshteyn, I.S., and...
Tài liệu Exchange 2007 part 13 docx
... Exchange 2007 Tài liệu dành cho học viên
VSIC Education Corporation Trang 99
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Exchange 2007 Tài liệu dành cho học viên
VSIC Education Corporation Trang 100
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Tài liệu Special Functions part 1 pptx
... 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 functi...
Tài liệu Special Functions part 2 doc
... 6.1 Gamma, Beta, and Related Functions
213
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... 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 SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... 1955,
Approximations...
Tài liệu Special Functions part 3 doc
... 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*(0.37409196+t*(0.09678418+
t*(-0.18628806+t*(0.27886807+t*(-1 .135 20398+t*(1.48851587+
t*(-0.82215223+t*0.17087277)))))))));
return x >= 0.0 ? ans : 2.0-ans;
}
There are also some functions of two variables that are special cases of the
incomplete ... (6.2.7) converges rapidly for x greater than about a+1...
Tài liệu Special Functions part 4 pdf
... 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 from NUMERICAL RECIPES IN ... 222
Chapter 6. Special Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... integral. Note that Ei(−x) is related to...
Tài liệu Special Functions part 11 pptx
... 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 from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... accurate approximations.
We will discuss the theory that leads to equation (6.10.3) later, in 13. 11, as
an interesting appl...
Tài liệu Special Functions part 12 doc
... x, x)=x
−1/2
(6.11 .13)
When the arguments are closeenough, the function is evaluatedfrom a fixedTaylor expansion
about (6.11 .13) through fifth-order terms. While the iterative part of the algorithm ... the first kind,
R
F
(x, y, z)=
1
2
∞
0
dt
(t + x)(t + y)(t + z)
(6.11.3)
262
Chapter 6. Special Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISB...
Tài liệu Special Functions part 5 ppt
... 226
Chapter 6. Special Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... function by modified Lentz’s
method (§5.2).
{
void nrerror(char error_text[]);
228
Chapter 6. Special Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... thisdoes not prove to be ve...
Tài liệu Special Functions part 6 pdf
... use the value 8),
approximate J
0
(x) and J
1
(x) by rational functions in x. Likewise approximate by
rational functions the “regular part of Y
0
(x) and Y
1
(x),definedas
Y
0
(x)−
2
π
J
0
(x)ln(x) ... 8.0) { Rational function approximation of (6.5.8).
y=x*x;
ans1=x*(-0.4900604943e13+y*(0.1275274390e13
+y*(-0.515343 8139 e11+y*(0.7349264551e9
+y*(-0.4237922726e7+y*0.8511937935e4)))));
ans...