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Once upon a time (1/t) pretty Poly Nomial was strolling across a field of vectors when she came to the edge of the singularly large matrix.

Now Polly was convergent, and her mother had made it an absolute condition that she must never enter such an array without her brackets on.
Polly, however, had changed her variables that morning and was feeling particularly badly behaved, and ignored this condition and made her way in amongst the complex elements.

Rows and columns enveloped her on all sides. Tangents approached her surface.
She became tensor and tensor. Quite suddenly, three branches of a hyperbola touched her at a single point.
She oscillated violently, lost all sense of Directrix, and went completely divergent.
As she reached a turning point she tripped over a square root which was protruding from the point and plunged headlong down a steep gradient. When she was differentiated once more she found herself, apparently alone, in a non-Euclidean space.

She was being watched, however. That smooth operator, Curly Pi, was lurking inner product. As his eyes devoured her curvilinear coordinates, a singular expression crossed his face. Was she still convergent he wondered? He decided to integrate improperly at once.

Hearing a vulgar fraction behind her, Polly turned around and saw Curly Pi approaching with his power series extrapolated. She could see it once, by his degenerate conic and his dissipative terms that he was bent on no good.

“Eureka!” she gasped.

“Ho ho,” he said. “What a symmetric little polynomial you are. I can see that are actually bubbling over with secs”.

“Oh Sir,” she protested. “keep away from me. I haven’t got my brackets on.”

“Calm yourself my dear.” Said our operator. “Your fears are purely imaginary.”

“i, i,” she thought “perhaps he’s homogeneous then.”

“What order are you?” he demanded.

“Seventeen” replied Poly.

Curley leered: “I suppose you’ve never been operated on yet?”

“Of course not!” Poly cried indignantly. “I’m absolutely convergent.”

“Come, come.” Said Curly. “Lets off to a decimal place I know where I’ll take
you to the limit.”

“Never!” gasped Poly.

“Calculus!” he swore, using the vilest oath he knew. His patience was gone.
Coshing her over the coefficient with a log until she was powerless, curly removed her discontinuities. He stared at her significant places and began
smoothing her points of inflexion. Poor Polly. All was up. She felt his hand tending to her asymototic limit. Her convergence would soon be gone forever.

There was no mercy, for curly was a Heavyside operator. He integrated by parts.
He integrated by partial fractions. The complex beast even went all the way around and multiply connected on her first integration. Curly without operating until he was absolutely and completely orthogonal.
When Polly got home that evening, her mother noticed that she had been truncated in several places. But it was too late to differentiate now. As the months went by, Polly increased monotonically. Finally she generated a small but pathological function, which lets surds all over the place until she was driven to distraction.

The moral of our sad story is this: if you want to keep your expressions convergent, never allow them a single degree of freedom.