FUNCTION:  ramamocktheta[getmockqs] - get q-expansion of mock theta function
 
CALLING SEQUENCE:  getmockqs(func,m)
 
PARAMETERS:   func -  char corresponding to a mock theta function
                 m -  integer (order of mock theta function)
 
GLOBAL VARIABLES:                     
SYNOPSIS:  
                    
EXAMPLES:  
                    
> with(ramamocktheta):
> with(qseries):
> f3q:=getmockqs(f,3):
> series(f3q,q,10);
                2      3      4      5      6      7      8      9      10
     1 + q - 2 q  + 3 q  - 3 q  + 3 q  - 5 q  + 7 q  - 6 q  + 6 q  + O(q  )

> qdegree(f3q);
                                      1001

> cf3:=n-> if type(n,integer) and n>=0 then coeff(f3q,q,n) else 0 fi:
> seq(cf3(125*n+99)+cf3(5*n+4),n=0..5);
    17500, -7237220, 680233240, -30719164585, 875359871775, -18035791352180

DISCUSSION:  
  We compute first few terms of the third order function f(q)
  Let c(n) be coefficient of q^n in f(q).
  It seems that
       c(125*n + 99) + c(5*n + 4) == 0 (mod 5)
                    
SEE ALSO:  

FUNCTION:  ramamocktheta[mockdesorder] - return list of mock theta functions of given order
 
CALLING SEQUENCE:  mockdesorder(m)
 
PARAMETERS:     m  -  integer (order of mock theta function)
 
GLOBAL VARIABLES:                     
SYNOPSIS:  
                    
EXAMPLES:  
                    
> with(ramamocktheta):
> mockdesorder(2):
There are 3 mock theta functions of order 2:
['A2', 'B2', 'mu2']

> mockdesorder(3):
There are 7 mock theta functions of order 3:
['f3', 'phi3', 'psi3', 'chi3', 'omega3', 'nu3', 'rho3']

> mockdesorder(5):
There are 12 mock theta functions of order 5:
['f05', 'f15', 'phi05', 'phi15', 'psi05', 'psi15', 'chi05', 'chi15', 'F05', 'F15', 'Psi05', 'Psi15']

> mockdesorder(6):
There are 9 mock theta functions of order 6:
['phi6', 'psi6', 'rho6', 'sigma6', 'lambda6', 'mu6', 'gamma6', 'phiminus6', 'psiminus6']

> mockdesorder(7):
There are 3 mock theta functions of order 7:
['F07', 'F17', 'F27']

> mockdesorder(8):
There are 8 mock theta functions of order 8:
['S08', 'S18', 'T08', 'T18', 'U08', 'U18', 'V08', 'V18']

> mockdesorder(10):
There are 4 mock theta functions of order 10:
['phi10', 'psi10', 'X10', 'chi10']> quit

DISCUSSION:  
   There are 7 mock functions of order 3.
   They are f(q), phi(q), psi(q), chi(q), omega(q), nu(q), rho(q)
                    
SEE ALSO:  
   

FUNCTION:  ramamocktheta[mockfuncdes] - description of a mock theta function
 
CALLING SEQUENCE:  mockfuncdes(func,m)
 
PARAMETERS:    func - char corresponds to a mock theta function
                  m - integer (order of a mock theta)
 
GLOBAL VARIABLES:                     
SYNOPSIS:  
                    
EXAMPLES:  
                    
> with(ramamocktheta):
> mockfuncdes(f,3);
"f3":
                                       /infinity          2       \
                                       | -----          (n )      |
                           1           |  \            q          |
            "f3" = ----------------- + |   )     -----------------|
                                   2   |  /                      2|
                   aqprod(-q, q, 0)    | -----   aqprod(-q, q, n) |
                                       \ n = 1                    /

DISCUSSION:  
  The definition of the third order mock theta function 
  f(q) = \sum_{n=0}^\infty \frac{ q^{n^2} }{(-q,q)_n^2}
                    
SEE ALSO:  

FUNCTION:  ramamocktheta[mockqs] - compute q-expansion of a given mock theta function
 
CALLING SEQUENCE:  mockqs(func,m,T)
 
PARAMETERS:    func - char corresponding to a mock theta function
                  m - integer (order of mock theta)   
                  T - positive integer
 
GLOBAL VARIABLES:                     
SYNOPSIS: Computes q-expansion of given order m function up to q^T  
                    
EXAMPLES:  
                    
> with(ramamocktheta):
> with(qseries):
> mockqs(f,3,10);
           2      3      4      5      6      7      8      9       10      11
1 + q - 2 q  + 3 q  - 3 q  + 3 q  - 5 q  + 7 q  - 6 q  + 6 q  - 10 q   + O(q  )

DISCUSSION:  
   We computed the first 10 terms of f(q) (third order function)
                    
SEE ALSO:  
   getmockqs

FUNCTION:  ramamocktheta[mockqtablemake] - update q-expansions of mock-theta functions in the package
 
CALLING SEQUENCE:  mockqtablepres(LT,LT1)
PARAMETERS:     LT  -  positive integer
                LT1 -  positive integer
 
GLOBAL VARIABLES: _mockqtable, _mockqtablepres, _mockqtableinds
                    
SYNOPSIS:  
   Compute q-expansions of all functions in package
   Most functions are computed to q^LT  (def with quad exponent)
                    
EXAMPLES:  
                    
> with(ramamocktheta):
> with(qseries):
> ramamocktheta[mockqtablemake](1000,300);          

DISCUSSION:  
                    
SEE ALSO:  
  getmockqs, mockqs

FUNCTION:  ramamocktheta[ramamockthetapversion] - package version
 
CALLING SEQUENCE:  ramamockthetapversion()
 
PARAMETERS:        -  
                   -  
 
GLOBAL VARIABLES:                     
SYNOPSIS:  
                    
EXAMPLES:  
                    
> with(ramamocktheta):
> ramamockthetapversion();
****************************************************
*
*  ramamocktheta  package version 0.1  
*  Thu, Jul 26, 2018  5:15:11 PM 
*  This version tested on MAPLE 2017
*
*  Please report any problems to fgarvan@ufl.edu
*  NO Previous versions:
        
****************************************************
DISCUSSION:  
                    
SEE ALSO: