Under Improve rs_series, you need to provide some idea of how you plan to 
implement at least a couple of those new rs_series functions that you 
suggest.
Maybe you could implement one of the comparatively simpler ones and send a 
PR for it.

Also you mentioned:

> I want to add more methods to ring_series so that its implementation is 
more smooth,fast and efficient.

You need to clarify this point a lot more. Which parts of the current 
implementation need improving and how do you plan to go about doing over 
the summer.
What gets more preference, improving the current implementation of existing 
functions or implementing new ones ?

Ditto for the other sections as well.

In the Timeline, you should provide a proper breakup of the tasks in the 
proposal and fairly appraise the time required for each. Most people 
provide a Week-wise breakup of the summer.

On Friday, March 29, 2019 at 11:08:12 AM UTC+5:30, Nabanita Dash wrote:
>
> I have added my application in wiki page . The link to which is 
> https://github.com/sympy/sympy/wiki/GSoC-2019-Nabanita-Dash:Series-expansions:Improving-rs_series,Formal-Power-Series(series.formal),limits(series.limits)
>
> On Wednesday, March 27, 2019 at 5:37:47 PM UTC+5:30, Nabanita Dash wrote:
>>
>>  Hi,
>> This is a GSoC-19 aspirant.I am a 2nd year CS Undergrad from 
>> IIIT,BBSR,India. I want to work on the project idea of Series-Expansion.I 
>> had discussed with Sartaj Singh as said by Aaron Meurer to geta hold on the 
>> idea.My proposed ideas are as below:
>> !)Improve rs_series module
>> I plan to add fourier,taylor,maclaurian,dirichlet,stirling series and 
>> other hyperbolic series in rs_series to make it efficient to use.
>> 2)Improve Formal Power Series
>> a)The limits applied to check fps and calculate logarithmic singularity 
>> needs improvement as it creates XFAIL tests.I want to create an API that 
>> accepts the singularities points and revise it to give positive results.
>> >>>f = asech(x)  
>> >>>fps(f, x) 
>> log(2) - log(x) - x**2/4 - 3*x**4/64 + O(x**6)
>>  A logarithmic singularity is a singularity of an analytic function whose 
>> main z-dependent term is of order O(lnz). An example is the singularity of 
>> the Bessel function of the second kind
>> Y_0(z)∼(2gamma)/pi+2/piln(1/2z)+... at z=0
>> ,Green function and some trignometric functions.
>>
>> Singularities with leading term consisting of nested logarithms, e.g., 
>> lnlnlnz, are also considered logarithmic.
>> 3) Improve limits
>> I think of adding special functions for calculating limits at oo. 
>> https://github.com/sympy/sympy/issues/14590 according to no special 
>> functions have been used in limits code.
>>
>> def test_exponential2():
>>     n = Symbol('n')
>>     assert limit((1 + x/(n + sin(n)))**n, n, oo) == exp(x)
>> Also,I plan to calculate limits at multivariate points.In SymP, 
>> limit(a,z,z0,dir='+') is possible to calculate limits for a single variable 
>> z,I want to calculate limit(f(x,y),x,y,x0,y0,dir='+')
>>
>>
>> I need suggestions to work on these ideas as well as any changes to be 
>> made to these or propose any other idea is welcome.
>>
>>

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