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| author | Patrik Müller <36931350+p1mueller@users.noreply.github.com> | 2022-04-20 09:19:09 +0200 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2022-04-20 09:19:09 +0200 |
| commit | fec8c22d82be501477980f716f7592171846808c (patch) | |
| tree | 1be997381cf0b734543afd63338faaf26e9becd6 /buch/chapters/050-differential | |
| parent | Start definition.tex (diff) | |
| parent | Singularitaeten (diff) | |
| download | SeminarSpezielleFunktionen-fec8c22d82be501477980f716f7592171846808c.tar.gz SeminarSpezielleFunktionen-fec8c22d82be501477980f716f7592171846808c.zip | |
Merge branch 'AndreasFMueller:master' into master
Diffstat (limited to 'buch/chapters/050-differential')
| -rw-r--r-- | buch/chapters/050-differential/besselhyper.maxima | 37 |
1 files changed, 37 insertions, 0 deletions
diff --git a/buch/chapters/050-differential/besselhyper.maxima b/buch/chapters/050-differential/besselhyper.maxima new file mode 100644 index 0000000..0a67819 --- /dev/null +++ b/buch/chapters/050-differential/besselhyper.maxima @@ -0,0 +1,37 @@ +/* + * besselhyper.maxima + */ +gradef(y(x), yp(x)); +gradef(yp(x), ypp(x)); + +w(x) := x^alpha * y(-x^2/4); + +/* Zusammenhang zwischen Y und W */ +Y: x^(-alpha) * W; + +/* erste Ableitung Yp ausgedrückt durch W und W' */ +e: Wp=diff(w(x),x) $ +e: ratsimp(e); +e: subst(W * x^(-alpha), y(-x^2/4), e) $ +e: subst(Yp, yp(-x^2/4), e) $ +s: solve(e, Yp) $ +Yp: rhs(s[1]) $ +Yp: ratsimp(Yp); +ratsimp(subst(0,W,Yp)); +ratsimp(subst(0,Wp,Yp)); + +/* zweite Ableitung Yp ausgedrückt durch W, W' und W'' */ +e: Wpp = ratsimp(diff(diff(w(x),x),x)); +e: subst(W * x^(-alpha), y(-x^2/4), e) $ +e: subst(Yp, yp(-x^2/4), e) $ +e: subst(Ypp, ypp(-x^2/4), e) $ +e: ratsimp(e) $ +Ypp: rhs(solve(e, Ypp)[1]) $ +Ypp: ratsimp(Ypp); +ratsimp(subst(0, W, subst(0, Wp, Ypp))); +ratsimp(subst(0, W, subst(0, Wpp, Ypp))); +ratsimp(subst(0, Wp, subst(0, Wpp, Ypp))); + + +B: (-x^2/4) * Ypp + (alpha+1)*Yp - Y; +expand(-x^(alpha+2) * B); |