### 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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