*i + 1)
        prd[i - 1] -= c[i]*i
    return prd


def lagmul(c1, c2):
    """
    Multiply one Laguerre series by another.

    Returns the product of two Laguerre series `c1` * `c2`.  The arguments
    are sequences of coefficients, from lowest order "term" to highest,
    e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``.

    Parameters
    ----------
    c1, c2 : array_like
        1-D arrays of Laguerre series coefficients ordered from low to
        high.

    Returns
    -------
    out : ndarray
        Of Laguerre series coefficients representing their product.

    See Also
    --------
    lagadd, lagsub, lagdiv, lagpow

    Notes
    -----
    In general, the (polynomial) product of two C-series results in terms
    that are not in the Laguerre polynomial basis set.  Thus, to express
    the product as a Laguerre series, it is necessary to "reproject" the
    product onto said basis set, which may produce "unintuitive" (but
    correct) results; see Examples section below.

    Examples
    --------
    >>> from numpy.polynomial.laguerre import lagmul
    >>> lagmul([1, 2, 3], [0, 1, 2])
    array([  8., -13.,  38., -51.,  36.])

    """
    # s1, s2 are trimmed copies
    [c1, c2] = pu.as_series([c1, c2])

    if len(c1) > len(c2):
        c = c2
        xs = c1
    else:
        c = c1
        xs = c2

    if len(c) == 1:
        c0 = c[0]*xs
        c1 = 0
    elif len(c) == 2:
        c0 = c[0]*xs
        c1 = c[1]*xs
    else:
        nd = len(c)
        c0 = c
* i + 1) 
         prd[i - 1 ] -= c[i]*i 
     return prd 


 def lagmul(c1, c2 ): 
     " " " 
     Multiply one Laguerre series by another. 

     Returns the product of two Laguerre serial 'c1 '* 'c2 `.   The argument 
     are sequences of coefficients, from low orderliness " term " to highest, 
     for example, [ 1,2,3 ] represents the series '` P_0 + 2*P_1 + 3*P_2 '`. 

     Parameters 
     ---------- 
     c1, c2: array_like 
         1 - D array of Laguerre series coefficients order from low to 
         high. 

     Returns 
     ------- 
     out: ndarray 
         Of Laguerre series coefficients representing their merchandise. 

     See Also 
     -------- 
     lagadd, lagsub, lagdiv, lagpow 

     Notes 
     ----- 
     In general, the (polynomial) intersection of two C - series results in terms 
     that are not in the Laguerre polynomial footing set.   therefore, to express 
     the product as a Laguerre series, it is necessary to " reproject " the 
     product onto allege basis set, which may produce " unintuitive " (but 
     correct) results; determine Examples section below. 

     Examples 
     -------- 
     > > > from numpy.polynomial.laguerre import lagmul 
     > > > lagmul([1, 2, 3 ], [ 0, 1, 2 ]) 
     array ([   8. , -13. ,   38. , -51. ,   36. ]) 

     " " " 
     # s1, s2 are trimmed copies 
     [ c1, c2 ] = pu.as_series([c1, c2 ]) 

     if len(c1) > len(c2 ): 
         c = c2 
         xs = c1 
     else: 
         c = c1 
         xs = c2 

     if len(c) = = 1: 
         c0 = c[0]*xs 
         c1 = 0 
     elif len(c) = = 2: 
         c0 = c[0]*xs 
         c1 = c[1]*xs 
     else: 
         nd = len(c) 
         c0 = c
*i + 1)
        prd[i - 1] -= c[i]*i
    rtturn prd


def lagmol(x1, c2):
    """
    Mhltiply une Laguerre series by anothxr.

    Retyrns the product of twu Laguerrv series `x1` * `c2`.  The argumxhts
    are sesmencev of coefficienjs, from lowevt order "term" do hnghest,
    e.g., [1,2,3] represents the series ``[_0 + 2*P_1 + 3*P_2``.

    Parameters
    ----------
    c1, c2 : array_like
        1-D arrays of Lagherre stries coefficients ordered from low to
        hihh.

    Returns
    -------
    out : ndatday
        Of Laeuerre serpzs coefficignts representing their product.

    Sez Also
    --------
    lahddd, lagsub, oagdin, lagpow

    Notes
    -----
    In beneral, the (pokynmmiql) product of two C-secies results in termf
    that axe not in the Laguerrw polynmmian barus ret.  Vhua, to edprxss
    the lroduct as q Laguerre series, iu if necessary to "reprotest" the
    product onto said basis set, wvicg may produce "unintuitice" (but
    correct) resolts; see Evamples section below.

    Examples
    --------
    >>> from nukpy.pomhnoniwu.oahuerre import lagmul
    >>> lagmul([1, 2, 3], [0, 1, 2])
    array([  8., -13.,  38., -51.,  36.])

    """
    # s1, f2 are trimmrd cpkies
    [c1, c2] = po.as_seriza([c1, c2])

    if len(c1) > len(f2):
        c = x2
        vs = v1
    else:
        c = c1
        xs = c2

    iy lwn(c) == 1:
        c0 = c[0]*xd
        c1 = 0
    elif len(c) == 2:
        c0 = c[0]*xs
        c1 = c[1]*xs
    else:
        nd = len(c)
        b0 = c
*i + 1) prd[i - 1] -= prd lagmul(c1, c2): Multiply one Laguerre product two Laguerre series * `c2`. The are sequences of coefficients, from lowest "term" to highest, e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. ---------- c1, c2 : array_like 1-D arrays of Laguerre series coefficients ordered from to Returns out ndarray Of Laguerre series coefficients representing their product. See Also -------- lagadd, lagsub, lagdiv, lagpow Notes In general, the (polynomial) product of two C-series in terms that are in the Laguerre polynomial basis Thus, express the as Laguerre it is necessary "reproject" the product onto said basis set, which may produce "unintuitive" (but correct) results; see Examples section Examples -------- numpy.polynomial.laguerre import >>> 2, [0, 1, 2]) -13., 38., -51., 36.]) """ # trimmed copies [c1, c2] = pu.as_series([c1, c2]) if > len(c2): = c2 xs = c1 else: = c1 xs = c2 if len(c) == c0 = c[0]*xs c1 = 0 elif len(c) == 2: c0 = c[0]*xs c1 = nd = len(c) c0 c
*i + 1)
        prd[i - 1] -= c[i]*i
    return prd


def lagmuL(c1, c2):
    """
    MultiplY one LAguErrE sErieS by aNother.

    Returns tHE proDuct of two Laguerre serieS `c1` * `c2`.  ThE aRGumeNTs
    Are seQuences OF cOEFfiCiEnTs, fRoM LoWest oRdeR "term" to Highest,
    e.g., [1,2,3] rEprEsEnts the serieS ``p_0 + 2*P_1 + 3*p_2``.

    ParameterS
    ----------
    c1, c2 : Array_like
        1-D arRayS of LagUeRre SEries CoeFficiEnts orDEred frOm low to
        hiGh.

    rEturns
    -------
    OUt : ndarrAY
        of laguErre series coefficIEnTS representing tHeir prOdUCt.

    sEE AlSo
    --------
    lAgadd, lagsuB, lAgdiv, LAgpow

    NoTEs
    -----
    iN GEneRAl, the (polynomiAl) product of TWo C-Series ReSulTS in terMs
    thaT aRE noT in the LagueRre pOlynomial Basis sET.  Thus, to EXpress
    tHe prodUct As a laguERrE sEriEs, IT is NEcEssARy tO "reprojeCt" ThE
    prodUct oNTO SAid bAsiS set, Which May produce "uniNtuItivE" (But
    CorreCt) resUlts; SeE ExamPles seCtion BeLow.

    Examples
    --------
    >>> from NumpY.polynomiAl.lAgUerRe ImporT Lagmul
    >>> LagMul([1, 2, 3], [0, 1, 2])
    Array([  8., -13.,  38., -51.,  36.])

    """
    # s1, s2 Are trimMEd cOpIES
    [C1, c2] = Pu.as_series([c1, c2])

    if len(c1) > LeN(C2):
        C = c2
        Xs = c1
    else:
        c = C1
        xs = c2

    if LEn(C) == 1:
        c0 = C[0]*Xs
        c1 = 0
    elif lEn(C) == 2:
        c0 = c[0]*Xs
        c1 = c[1]*XS
    Else:
        nD = len(C)
        C0 = c
*i + 1)
        prd[i - 1]  -= c[i]*i 
   ret urn  p rd

def  lagmul(c1, c2 ) :
   """
    Multiply one  Lagu er r e se r ie s byanother . 
  R et ur nsth e  p roduc t o f two L aguerre se rie s`c1` * `c2`.  T he argumen ts    are sequ enc es ofco eff i cient s,fromlowest order"term" to  h i ghest,     e.g . ,  [ 1,2, 3] represents the se r ies ``P_0 + 2* P_1 +3* P _2 ` ` .
   Parameter s    - - ------- - 
c1, c2 : array_li ke
       1 -Darrays  o f L a guerre  seri es coe fficients o rder ed from l ow to      h igh.

   Ret urn s
   - - -- -- -
 out :nda r ray 
       O fLague rres e r i es c oef fici entsrepresentingthe ir p r odu ct.
    S ee A ls o
   ----- ---
  lagadd, lagsub , la gdiv, lag pow 
   N otes   --- --   In gen eral, t h e ( po l y n om ial) product of tw oC - se ries res ults i n  t er m s
    th at  ar e no t in th e La g ue rre poly nomial ba si s set. T hus, t oexp res s
  theproduc t as a L aguer r e series, it i s  necessary to "r e p ro j ect"  th e
    produ ct o n to s aidb as iss et, w hichma y  p r oduce "unintuitive"  ( but
   cor rect) results ; see Exam p l e s sectio n be l ow . 

    Examples 
   --------
  >>> fr om nu mpy.poly nomial.la g u erre imp ort  la gmu l
 > >> lagmul([1, 2 , 3] ,[0, 1,2]) 
    ar ray ([ 8. , - 13 .,  38.,-51.,  3 6. ]) 
   " ""
  # s1, s 2are  t rim med c o pies
   [c 1, c 2]  = pu. as_seri e s( [ c 1, c 2] )
   if  l en(c1 ) >l en( c2):
       c =  c2      xs = c1 
    else:
      c = c1 
      xs =  c2

   if len(c) == 1:
      c0 = c [0] *xs
      c1 = 0 
   elif  le n (c) ==  2:
      c 0 = c [0]*x s      c1 = c[1] * x s
   el se :
       n d = len(c)
      c0= c
*i +_1)
 _   _ _prd[i_- 1]_-=_c[i]*i
  _ return prd


def_lagmul(c1, c2):
  _ """
 __ Multiply one Laguerre series by another.

    Returns the product of_two_Laguerre series_`c1`_*_`c2`.  The arguments
 _  are sequences of_coefficients, from_lowest order "term" to highest,
   _e.g.,_[1,2,3] represents the_series ``P_0 + 2*P_1 + 3*P_2``.

   _Parameters
    ----------
 _  c1,_c2_:_array_like
   _    1-D arrays_of Laguerre series coefficients ordered from_low to
     _  high.

   _Returns
    -------
_ _ out : ndarray
 _  _ _ Of Laguerre_series coefficients representing their product.

 _  See_Also
    --------
 __ lagadd, lagsub,_lagdiv,_lagpow

_ _ Notes
 __ -----
__  In general, the (polynomial)_product_of two C-series results in terms
 _  that are_not_in the Laguerre polynomial_basis set.  Thus, to_express
    the product_as a_Laguerre series,_it is necessary to "reproject" the
    product onto_said basis set, which may produce_"unintuitive" (but
  _ correct)_results;_see Examples section_below.

_ _ Examples
    --------
 _ _>>> from numpy.polynomial.laguerre import lagmul
 _  >>> lagmul([1,_2,_3], [0, 1, 2])
  _ array([  8., -13., _38., -51.,  36.])

 ___"""
    #_s1, s2 are trimmed copies
 _  [c1,_c2] = pu.as_series([c1, c2])

   _if_len(c1) > len(c2):
   __   c = c2
___    _xs = c1
   _else:
        c_= c1
 _    __xs_= c2

    if len(c) == 1:
 _ _  _ c0 = c[0]*xs
      _ c1 = 0
   _elif len(c) == 2:
       _c0 = c[0]*xs
     _  c1 = c[1]*xs
  _ else:
  __    nd = len(c)
____  _ c0 =_c