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XCas sum limit confusion
09-02-2023, 12:54 PM
Post: #3
RE: XCas sum limit confusion
For the same reason, product limits behave exactly the same as sum.

Cas> Pochhammer(a,n) := product((a+j), j, 0, n-1)
Cas> Pochhammer(a, 0)      → 1
Cas> Pochhammer(0, 0)      → 1

When limits get switched, "opposite" for sum negated equivalent to product reciprocal.

Pochhammer(a, -|n|) = product((a+j), j, 0, -|n|-1) = 1/product((a+j), j, -|n|, -1)

Cas> Pochhammer(a, 3)      → a*(a+1)*(a+2)
Cas> Pochhammer(a, -3)     → 1/((a-1)*(a-2)*(a-3))
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Messages In This Thread
XCas sum limit confusion - Albert Chan - 08-26-2020, 07:48 PM
RE: XCas sum limit confusion - Albert Chan - 08-26-2020, 09:58 PM
RE: XCas sum limit confusion - Albert Chan - 09-02-2023 12:54 PM



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