Nuprl Definition : fps-div-coeff
fps-div-coeff(eq;r;f;g;x;b)
==r x * (f[b] +r (-r Σ(p∈[p∈bag-partitions(eq;b)|¬bbag-null(fst(p))]). g[fst(p)] * fps-div-coeff(eq;r;f;g;x;snd(p))))
fps-div-coeff(eq;r;f;g;x;b) ==
fix((λfps-div-coeff,b. (x
*
(f[b]
+r
(-r Σ(p∈[p∈bag-partitions(eq;b)|¬bbag-null(fst(p))]). g[fst(p)] * (fps-div-coeff (snd(p))))))\000C))
b
Definitions occuring in Statement :
fps-coeff: f[b],
bag-partitions: bag-partitions(eq;bs),
bag-summation: Σ(x∈b). f[x],
bag-null: bag-null(bs),
bag-filter: [x∈b|p[x]],
bnot: ¬bb,
infix_ap: x f y,
pi1: fst(t),
pi2: snd(t),
apply: f a,
fix: fix(F),
lambda: λx.A[x],
rng_times: *,
rng_minus: -r,
rng_zero: 0,
rng_plus: +r
Definitions occuring in definition :
fix: fix(F),
lambda: λx.A[x],
rng_minus: -r,
bag-summation: Σ(x∈b). f[x],
rng_zero: 0,
rng_plus: +r,
bag-filter: [x∈b|p[x]],
bag-partitions: bag-partitions(eq;bs),
bnot: ¬bb,
bag-null: bag-null(bs),
infix_ap: x f y,
rng_times: *,
fps-coeff: f[b],
pi1: fst(t),
apply: f a,
pi2: snd(t)
FDL editor aliases :
fps-div-coeff
Latex:
fps-div-coeff(eq;r;f;g;x;b)
==r x
*
(f[b]
+r
(-r
\mSigma{}(p\mmember{}[p\mmember{}bag-partitions(eq;b)|\mneg{}\msubb{}bag-null(fst(p))])
g[fst(p)] * fps-div-coeff(eq;r;f;g;x;snd(p))))
Latex:
fps-div-coeff(eq;r;f;g;x;b) ==
fix((\mlambda{}fps-div-coeff,b. (x
*
(f[b]
+r
(-r
\mSigma{}(p\mmember{}[p\mmember{}bag-partitions(eq;b)|\mneg{}\msubb{}bag-null(fst(p))]). g[fst(p)]
*
(fps-div-coeff
(snd(p))))))))
b
Date html generated:
2016_05_15-PM-09_48_29
Last ObjectModification:
2015_09_23-AM-08_21_15
Theory : power!series
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