mingamma.gms : Minimal y of GAMMA(x)
Find minimum of y=gamma(x) and y=loggamma(x) for x>0
Reference:
- Sloane, N J A, The On-Line Encyclopedia of Integer Sequences; Sequence A030169. http://www.research.att.com/projects/OEIS?Anum=A030169
Small Model of Type: DNLP
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$Title Minimal y of GAMMA(x) (MINGAMMA,SEQ=299)
$ontext
Find minimum of y=gamma(x) and y=loggamma(x) for x>0
Sloane, N J A, The On-Line Encyclopedia of Integer Sequences; Sequence
A030169. http://www.research.att.com/projects/OEIS?Anum=A030169
$offtext
variables y1,y2,x1,x2;
equations y1def,y2def;
x1.lo = 0.01; x2.lo = 0.01;
y1def.. y1 =e= gamma(x1);
y2def.. y2 =e= loggamma(x2);
model m1 /y1def/
m2 /y2def/;
solve m1 minimizing y1 using dnlp;
solve m2 minimizing y2 using nlp;
scalar x1opt / 1.46163214496836 /, x1delta, x2delta
y1opt / 0.8856031944108887 /, y1delta, y2delta
y2opt;
y2opt := log(y1opt);
option decimals=8;
x1delta = x1.l - x1opt; y1delta = y1.l - y1opt;
x2delta = x2.l - x1opt; y2delta = y2.l - y2opt;
display x1.l,x2.l,y1.l,y2.l,x1opt,y1opt,y2opt,
x1delta,x2delta,y1delta,y2delta;
scalar tol / 1e-6 /;
abort$(abs(x1delta) > tol or abs(x2delta) > tol or
abs(y1delta) > tol or abs(y2delta) > tol ) "inconsistent results";
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