       Questions about series and O[x]

• To: mathgroup at smc.vnet.net
• Subject: [mg12782] Questions about series and O[x]
• From: 6500mdl0 at ucsbuxa.ucsb.edu (Matthew D Litwin)
• Date: Wed, 10 Jun 1998 03:04:42 -0400
• Organization: University of California, Santa Barbara
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I'm working with series with fractional exponents, and have a few
questions on how to efficiently do certain operations.

1) Suppose you have a series like f=1 +x^(1/2) +x + x^(3/2) +O[x]^2 What
is the most efficient way to apply a transformation like  x -> x^(2/3)
which would yield a series with order O[x]^(4/3). The best I've found
is to operate on Normal[f] and add the O[x] term by hand, but this
seems slower than it need be for long series.

2) Suppose you have two (or three) such series and are taking the
product, call it P, and you know that the only non-zero terms in P are
of the form A x^n, where n is an integer. Is there any way to avoid
computing the fractional terms in P?

Thank you for any suggestions,

-Matt Litwin
matt at math.ucsb.edu

```

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