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gh-38093: add doc on egf_to_ogf and inverse Just adding a little comment in the doc on the link to Borel and Laplace formal transforms. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have updated the documentation and checked the documentation preview. URL: #38093 Reported by: Frédéric Chapoton Reviewer(s): Matthias Köppe
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src/sage/rings/power_series_ring_element.pyx

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@@ -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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This function is known as :pari:`serlaplace` in PARI/GP.
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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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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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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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