@@ -2764,9 +2764,13 @@ cdef class PowerSeries(AlgebraElement):
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def egf_to_ogf (self ):
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r """
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Return the ordinary generating function power series,
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- assuming self is an exponential generating function power series.
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+ assuming `` self`` is an exponential generating function power series.
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- This function is known as ``serlaplace`` in PARI/GP.
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+ This is a formal Laplace transform.
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+
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+ This function is known as :pari:`serlaplace` in PARI/GP.
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+
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+ .. SEEALSO:: :meth:`ogf_to_egf` for the inverse method.
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EXAMPLES::
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@@ -2775,23 +2779,27 @@ cdef class PowerSeries(AlgebraElement):
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sage: f. egf_to_ogf( )
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t + t^ 2 + 2* t^ 3
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"""
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- return self .parent()([self [i] * arith.factorial(i) for i in range (self .degree()+ 1 )])
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+ return self .parent()([self [i] * arith.factorial(i) for i in range (self .degree() + 1 )])
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def ogf_to_egf (self ):
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r """
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Return the exponential generating function power series,
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- assuming self is an ordinary generating function power series.
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+ assuming ``self`` is an ordinary generating function power series.
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+
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+ This is a formal Borel transform.
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This can also be computed as ``serconvol( f,exp( t)) `` in PARI/GP.
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+ .. SEEALSO:: :meth:`egf_to_ogf` for the inverse method.
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+
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EXAMPLES::
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sage: R. <t> = PowerSeriesRing( QQ)
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sage: f = t + t^ 2 + 2* t^ 3
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sage: f. ogf_to_egf( )
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t + 1/2* t^ 2 + 1/3* t^ 3
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"""
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- return self .parent()([self [i] / arith.factorial(i) for i in range (self .degree()+ 1 )])
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+ return self .parent()([self [i] / arith.factorial(i) for i in range (self .degree() + 1 )])
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def __pari__ (self ):
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"""
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