@anutosh491 I have now fixed the `e.is_zero` case. Also added tests for this and the e<0 case.

In [1]: besselk(1,cos(x)).as_leading_term(x)
Out[1]: besselk(1, 1)

In [2]: besselk(3,1/x).as_leading_term(x)
Out[2]: 
       -1 
       ───
        x 
√2⋅√π⋅ℯ   
──────────
      ___ 
     ╱ 1  
2⋅  ╱  ─  
  ╲╱   x  

In [9]: besselk(3,1/sin(x)).as_leading_term(x)
Out[9]: 
       -1 
       ───
        x 
√2⋅√π⋅ℯ   
──────────
      ___ 
     ╱ 1  
2⋅  ╱  ─  
  ╲╱   x  

In [8]: besselk(3,1/sin(x)).series(x, n=1).expand().removeO()
Out[8]: 
        -1    
       ────── 
       sin(x) 
√2⋅√π⋅ℯ       
──────────────
      ________
     ╱   1    
2⋅  ╱  ────── 
  ╲╱   sin(x)