docs: minor docstring fixes

docs/sources/exploring-continued-fractions.rst

@@ -107,7 +107,7 @@ It is also possible to get all of the convergents at once using the :py:attr:`~c
    >>> tuple(ContinuedFraction(649 200).convergents)
    ((0, ContinuedFraction(3, 1)), (1, ContinuedFraction(13, 4)), (2, ContinuedFraction(159, 49)), (3, ContinuedFraction(649, 200)))
 
-The return of a generator of an enumerated sequence is helpful as it allows the caller to define an appropriate static data structure to store all the convergents, if required, e.g. via a dict keyed by convergent index :math:`0, 1,\ldots, n`.
+The return of a generator of an enumerated sequence is helpful as it allows the caller to define an appropriate static data structure to store all the convergents by index, if required, e.g. via a dict:
 
 .. code:: python
 
@@ -127,7 +127,7 @@ It is known that even- and odd-indexed convergents behave differently: the even-
 
    \frac{p_k}{q_k} - \frac{p_{k - 1}}{q_{k - 1}} = \frac{(-1)^k}{q_kq_{k - 1}}, \hskip{3em} k \geq 1
 
-The :py:class:`~continuedfractions.continuedfraction.ContinuedFraction` class provides (cached) properties for even-indexed convergents (:py:attr:`~continuedfractions.continuedfraction.ContinuedFraction.even_convergents`) and odd-indexed convergents (:py:attr:`~continuedfractions.continuedfraction.ContinuedFraction.odd_convergents`), as illustrated below.
+The :py:class:`~continuedfractions.continuedfraction.ContinuedFraction` class provides properties for generating even-indexed convergents (:py:attr:`~continuedfractions.continuedfraction.ContinuedFraction.even_convergents`) and odd-indexed convergents (:py:attr:`~continuedfractions.continuedfraction.ContinuedFraction.odd_convergents`), as illustrated below.
 
 .. code:: python
 

src/continuedfractions/continuedfraction.py

@@ -744,7 +744,10 @@ def convergents(self) -> Generator[tuple[int, ContinuedFraction], None, None]:
 
         The convergents are generated as tuples of :py:class:`int` and
         :py:class:`~continuedfraction.continuedfraction.ContinuedFraction`
-        instances, where the integers represent the orders of the convergents.
+        instances, where the integers represent the indices of the convergents.
+
+        If :math:`n` is the order of the continued fraction then :math:`n + 1`
+        convergents :math:`C_0, C_1, \\ldots, C_n` are generated in that order.
 
         Yields
         ------
@@ -765,9 +768,12 @@ def convergents(self) -> Generator[tuple[int, ContinuedFraction], None, None]:
     def even_convergents(self) -> Generator[tuple[int, ContinuedFraction], None, None]:
         """Generates an enumerated sequence of all even-order convergents of the continued fraction.
 
-        The even-order convergents are generated as tuples of :py:class:`int`
-        and :py:class:`~continuedfraction.continuedfraction.ContinuedFraction`
-        instances, where the integers represent the orders of the convergents.
+        The convergents are generated as tuples of :py:class:`int` and
+        :py:class:`~continuedfraction.continuedfraction.ContinuedFraction`
+        instances, where the integers represent the indices of the convergents.
+
+        If :math:`n` is the order of the continued fraction then only the even-
+        indexed convergents :math:`C_0, C_2, C_4, \\ldots` are generated.
 
         Yields
         ------
@@ -787,9 +793,12 @@ def even_convergents(self) -> Generator[tuple[int, ContinuedFraction], None, Non
     def odd_convergents(self) -> Generator[tuple[int, ContinuedFraction], None, None]:
         """Generates an enumerated sequence of all odd-order convergents of the continued fraction.
 
-        The odd-order convergents are generated as tuples of :py:class:`int`
-        and :py:class:`~continuedfraction.continuedfraction.ContinuedFraction`
-        instances, where the integers represent the orders of the convergents.
+        The convergents are generated as tuples of :py:class:`int` and
+        :py:class:`~continuedfraction.continuedfraction.ContinuedFraction`
+        instances, where the integers represent the indices of the convergents.
+
+        If :math:`n` is the order of the continued fraction then only the odd-
+        indexed convergents :math:`C_1, C_3, C_5, \\ldots` are generated.
 
         Yields
         ------

src/continuedfractions/lib.py

@@ -309,8 +309,8 @@ def convergents(*elements: int) -> Generator[Fraction, None, None]:
     """Generates an (ordered) sequence of convergents of a (finite, simple) continued fraction given as a sequence of its elements.
 
     If :math:`n` is the order of the continued fraction represented by the
-    given sequence of its elements then convergents of orders
-    :math:`0, 1, \\ldots, n` are generated in that order.
+    given sequence of its elements then :math:`n + 1` convergents
+    :math:`C_0, C_1, \\ldots, C_n` are generated in that order.
 
     Parameters
     ----------
@@ -322,7 +322,7 @@ def convergents(*elements: int) -> Generator[Fraction, None, None]:
     ------
     fractions.Fraction
         Each element generated is a :py:class:`fractions.Fraction` instance and
-        a :math:`k`-order convergent of the given continued fraction.
+        a :math:`k`-th convergent of the given continued fraction.
 
     Raises
     ------