function [besk0eresult,x]=besk0e(x);
besk0eresult=[];
persistent ak02cs ak0cs besk0e bk0cs first firstCall ntak0 ntak02 ntk0 xsml y ; if isempty(firstCall),firstCall=1;end;
if isempty(ak02cs), ak02cs=zeros(1,14); end;
if isempty(ak0cs), ak0cs=zeros(1,17); end;
if isempty(besk0eresult), besk0eresult=0; end;
if isempty(bk0cs), bk0cs=zeros(1,11); end;
if isempty(xsml), xsml=0; end;
if isempty(y), y=0; end;
if isempty(ntak0), ntak0=0; end;
if isempty(ntak02), ntak02=0; end;
if isempty(ntk0), ntk0=0; end;
%***BEGIN PROLOGUE BESK0E
%***PURPOSE Compute the exponentially scaled modified (hyperbolic)
% Bessel function of the third kind of order zero.
%***LIBRARY SLATEC (FNLIB)
%***CATEGORY C10B1
%***TYPE SINGLE PRECISION (BESK0E-S, DBSK0E-D)
%***KEYWORDS EXPONENTIALLY SCALED, FNLIB, HYPERBOLIC BESSEL FUNCTION,
% MODIFIED BESSEL FUNCTION, ORDER ZERO, SPECIAL FUNCTIONS,
% THIRD KIND
%***AUTHOR Fullerton, W., (LANL)
%***DESCRIPTION
%
% BESK0E(X) computes the exponentially scaled modified (hyperbolic)
% Bessel function of third kind of order zero for real argument
% X .GT. 0.0, i.e., EXP(X)*K0(X).
%
% Series for BK0 on the interval 0. to 4.00000D+00
% with weighted error 3.57E-19
% log weighted error 18.45
% significant figures required 17.99
% decimal places required 18.97
%
% Series for AK0 on the interval 1.25000D-01 to 5.00000D-01
% with weighted error 5.34E-17
% log weighted error 16.27
% significant figures required 14.92
% decimal places required 16.89
%
% Series for AK02 on the interval 0. to 1.25000D-01
% with weighted error 2.34E-17
% log weighted error 16.63
% significant figures required 14.67
% decimal places required 17.20
%
%***REFERENCES (NONE)
%***ROUTINES CALLED BESI0, CSEVL, INITS, R1MACH, XERMSG
%***REVISION HISTORY (YYMMDD)
% 770401 DATE WRITTEN
% 890531 Changed all specific intrinsics to generic. (WRB)
% 890531 REVISION DATE from Version 3.2
% 891214 Prologue converted to Version 4.0 format. (BAB)
% 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
% 900326 Removed duplicate information from DESCRIPTION section.
% (WRB)
%***end PROLOGUE BESK0E
if isempty(first), first=false; end;
if firstCall, bk0cs(1)=[-.03532739323390276872e0]; end;
if firstCall, bk0cs(2)=[.3442898999246284869e0]; end;
if firstCall, bk0cs(3)=[.03597993651536150163e0]; end;
if firstCall, bk0cs(4)=[.00126461541144692592e0]; end;
if firstCall, bk0cs(5)=[.00002286212103119451e0]; end;
if firstCall, bk0cs(6)=[.00000025347910790261e0]; end;
if firstCall, bk0cs(7)=[.00000000190451637722e0]; end;
if firstCall, bk0cs(8)=[.00000000001034969525e0]; end;
if firstCall, bk0cs(9)=[.00000000000004259816e0]; end;
if firstCall, bk0cs(10)=[.00000000000000013744e0]; end;
if firstCall, bk0cs(11)=[.00000000000000000035e0]; end;
if firstCall, ak0cs(1)=[-.07643947903327941e0]; end;
if firstCall, ak0cs(2)=[-.02235652605699819e0]; end;
if firstCall, ak0cs(3)=[.00077341811546938e0]; end;
if firstCall, ak0cs(4)=[-.00004281006688886e0]; end;
if firstCall, ak0cs(5)=[.00000308170017386e0]; end;
if firstCall, ak0cs(6)=[-.00000026393672220e0]; end;
if firstCall, ak0cs(7)=[.00000002563713036e0]; end;
if firstCall, ak0cs(8)=[-.00000000274270554e0]; end;
if firstCall, ak0cs(9)=[.00000000031694296e0]; end;
if firstCall, ak0cs(10)=[-.00000000003902353e0]; end;
if firstCall, ak0cs(11)=[.00000000000506804e0]; end;
if firstCall, ak0cs(12)=[-.00000000000068895e0]; end;
if firstCall, ak0cs(13)=[.00000000000009744e0]; end;
if firstCall, ak0cs(14)=[-.00000000000001427e0]; end;
if firstCall, ak0cs(15)=[.00000000000000215e0]; end;
if firstCall, ak0cs(16)=[-.00000000000000033e0]; end;
if firstCall, ak0cs(17)=[.00000000000000005e0]; end;
if firstCall, ak02cs(1)=[-.01201869826307592e0]; end;
if firstCall, ak02cs(2)=[-.00917485269102569e0]; end;
if firstCall, ak02cs(3)=[.00014445509317750e0]; end;
if firstCall, ak02cs(4)=[-.00000401361417543e0]; end;
if firstCall, ak02cs(5)=[.00000015678318108e0]; end;
if firstCall, ak02cs(6)=[-.00000000777011043e0]; end;
if firstCall, ak02cs(7)=[.00000000046111825e0]; end;
if firstCall, ak02cs(8)=[-.00000000003158592e0]; end;
if firstCall, ak02cs(9)=[.00000000000243501e0]; end;
if firstCall, ak02cs(10)=[-.00000000000020743e0]; end;
if firstCall, ak02cs(11)=[.00000000000001925e0]; end;
if firstCall, ak02cs(12)=[-.00000000000000192e0]; end;
if firstCall, ak02cs(13)=[.00000000000000020e0]; end;
if firstCall, ak02cs(14)=[-.00000000000000002e0]; end;
if firstCall, first=[true]; end;
firstCall=0;
%***FIRST EXECUTABLE STATEMENT BESK0E
if( first )
[ntk0 ,bk0cs]=inits(bk0cs,11,0.1.*r1mach(3));
[ntak0 ,ak0cs]=inits(ak0cs,17,0.1.*r1mach(3));
[ntak02 ,ak02cs]=inits(ak02cs,14,0.1.*r1mach(3));
xsml = sqrt(4.0.*r1mach(3));
end;
first = false;
%
if( x<=0. )
xermsg('SLATEC','BESK0E','X IS ZERO OR NEGATIVE',2,2);
end;
if( x>2. )
%
if( x<=8. )
besk0eresult =(1.25+csevl((16../x-5.)./3.,ak0cs,ntak0))./sqrt(x);
end;
if( x>8. )
besk0eresult =(1.25+csevl(16../x-1.,ak02cs,ntak02))./sqrt(x);
end;
else;
%
y = 0.;
if( x>xsml )
y = x.*x;
end;
besk0eresult = exp(x).*(-log(0.5.*x).*besi0(x)-.25+csevl(.5.*y-1.,bk0cs,ntk0));
csnil=dbstack(1); csnil=csnil(1).name(1)~='@';
if csnil&&~isempty(inputname(1)), assignin('caller','FUntemp',x); evalin('caller',[inputname(1),'=FUntemp;']); end
return;
end;
%
csnil=dbstack(1); csnil=csnil(1).name(1)~='@';
if csnil&&~isempty(inputname(1)), assignin('caller','FUntemp',x); evalin('caller',[inputname(1),'=FUntemp;']); end
end
%DECK BESK0
