1 | initial version |

A trivial, brute-force solution to get a Latex expression of this series :

```
# The function
sage: f=(x/sqrt(x^2-6*x+13))
Its requested Taylor series
sage: %time s=f.taylor(x,4,1000)
CPU times: user 5.57 s, sys: 11.9 ms, total: 5.58 s
Wall time: 5.29 s
# Latex each ot its terms
sage: %time t=list(map(lambda u:str(latex(u)), reversed(s.operands())))
CPU times: user 59.2 ms, sys: 83 µs, total: 59.3 ms
Wall time: 59.3 ms
# Latex of the series
sage: %time p = " + ".join(t)
CPU times: user 127 µs, sys: 0 ns, total: 127 µs
Wall time: 133 µs
```

which I won't try to print since it would require about

```
sage: ceil(len(p)/35/60)
274
```

274 pages typeset at 60 characters per line on 35 lines per page.

Note that the result you'll get will express the development in terms of powers of $x-4$ ; if you need it in terms of $x$, try the same trick on `se = s.expand()`

. This will tell you that the $x^{1000}$ coefficient is about $1.3\cdot10^{352}$.

What are you trying to do ? Frighten the horses ?

HTH,

2 | No.2 Revision |

A trivial, brute-force solution to get a Latex expression of this series :

```
# The function
sage: f=(x/sqrt(x^2-6*x+13))
Its requested Taylor series
sage: %time s=f.taylor(x,4,1000)
CPU times: user 5.57 s, sys: 11.9 ms, total: 5.58 s
Wall time: 5.29 s
# Latex each ot its terms
sage: %time t=list(map(lambda u:str(latex(u)), reversed(s.operands())))
CPU times: user 59.2 ms, sys: 83 µs, total: 59.3 ms
Wall time: 59.3 ms
# Latex of the series
sage: %time p = " + ".join(t)
CPU times: user 127 µs, sys: 0 ns, total: 127 µs
Wall time: 133 µs
```

which I won't try to print since it would require about

```
sage: ceil(len(p)/35/60)
274
```

274 pages typeset at 60 characters per line on 35 lines per page.

Note that the result you'll get will express the development in terms of powers of $x-4$ ; if you need it in terms of $x$, try the same trick on `se = s.expand()`

. This will tell you that the $x^{1000}$ coefficient is about ~~$1.3\cdot10^{352}$.~~$1.3\cdot10^{-352}$.

What are you trying to do ? Frighten the horses ?

HTH,

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