Implemented _eval_nseries() for Hyper

[dhruvmendiratta6]

References to other Issues or PRs

Fixes #18193

Brief description of what is fixed or changed

In reference to Issue #18193 the function was implemented. Example of
the working code is as follows:

In [1]: from sympy import hyper

In [2]: from sympy.abc import x, y

In [3]: hyper((1, 2),(1, 2), x)._eval_nseries(x, 7, y)
Out[3]: 1 + x + x2/2 + x3/6 + x4/24 + x5/120 + x6/720 + O(x7)

In [4]: hyper((1, 2),(3, 4, 5), x)._eval_nseries(x, 7, y)
Out[4]: 1 + x/30 + x2/1200 + x3/63000 + x4/4233600 + x5/355622400 + x6/36578304000 + O(x7)

Other comments

Release Notes

• functions
  • Added _eval_nseries() functionality to hyper

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• functions
  • Added _eval_nseries() functionality to hyper (#18630 by @dhruvmendiratta6)

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#### References to other Issues or PRs
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Fixes #18193 

#### Brief description of what is fixed or changed
In reference to Issue #18193 the function was implemented. Example of
the working code is as follows:

In [1]: from sympy import hyper

In [2]: from sympy.abc import x, y

In [3]: hyper((1, 2),(1, 2), x)._eval_nseries(x, 7, y)
Out[3]: 1 + x + x**2/2 + x**3/6 + x**4/24 + x**5/120 + x**6/720 + O(x**7)

In [4]: hyper((1, 2),(3, 4, 5), x)._eval_nseries(x, 7, y)
Out[4]: 1 + x/30 + x**2/1200 + x**3/63000 + x**4/4233600 + x**5/355622400 + x**6/36578304000 + O(x**7)


#### Other comments


#### Release Notes

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<!-- BEGIN RELEASE NOTES -->
* functions
   * Added _eval_nseries() functionality to hyper
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[oscarbenjamin]

This will need tests

[dhruvmendiratta6]

Actually the following test is still failing. I committed it anyway as the code is working and I couldn't figure out what was going wrong.
File "c:\users\mendiratta\sympy\sympy\functions\special\tests\test_hyper.py", line 347, in test_limits O(k**6) # issue 6350 AssertionError

[jksuom]

There a a couple of things that should be changed in the code. In the failing issue, the argument of the function is k**2 so that is what should appear in the series expansion. Also I think that self should be added to the super() call. Then it should be possible to fix the failing test.

[jksuom]

Suggested change

	return super()._eval_nseries(x, n, logx)
	return super()._eval_nseries(self, x, n, logx)

[jksuom]

I'm not sure of this, though. The docs say that if the second argument of super is omitted, then the method will be unbound but I don't know what will happen if both arguments are omitted. However, there is an example that seems to indicate that the returned method will be bound to self. Perhaps that should be tested.

[jksuom]

Tests seem to show that the method will be bound. So better leave this unchanged.

[dhruvmendiratta6]

I think what you are saying is the way it was done in python 2 and in python 3 both the arguments can be left omitted.

[jksuom]

Actually, terms should be computed with expansion of arg as a series in x, but that is not needed for the existing tests.

[dhruvmendiratta6]

After removing self argument from super()._eval_nseries() call which was added by mistake there are some differences while calling the _eval_nseries() of hyper and exp which are as follows:

>>> hyper((1,2),(1,2), x)._eval_nseries(y,7,None)
hyper((1, 2), (1, 2), x) + O(y**7)

>>> exp(x)._eval_nseries(y,7,None)
exp(x)

>>> exp(x**2)._eval_nseries(x,7,None)
1 + x**2 + x**4/2 + x**6/6 + x**8/24 + x**10/120 + x**12/720 + O(x**14)

>>> hyper((1,2),(1,2), x**2)._eval_nseries(x,7,None)
1 + x**2 + x**4/2 + x**6/6 + O(x**7)

is the test failing due to the difference in second output. As what I understood was that maximum power of x can be of the order of n but that is not the case with exp._eval_nseries()

[codecov]

Codecov Report

Merging #18630 into master will decrease coverage by 8.053%.
The diff coverage is 100%.

@@              Coverage Diff              @@
##            master    #18630       +/-   ##
=============================================
- Coverage   75.322%   67.268%   -8.054%     
=============================================
  Files          640       644        +4     
  Lines       167174    167831      +657     
  Branches     39426     39565      +139     
=============================================
- Hits        125919    112897    -13022     
- Misses       35721     49459    +13738     
+ Partials      5534      5475       -59

[jksuom]

Thanks, this is ready to be merged.