diff --git a/docs/source/python/api/arrays.rst b/docs/source/python/api/arrays.rst
index dc24be8bd06..290ce09befb 100644
--- a/docs/source/python/api/arrays.rst
+++ b/docs/source/python/api/arrays.rst
@@ -29,12 +29,21 @@ These functions create new Arrow arrays:
 .. autosummary::
    :toctree: ../generated/
 
+   arange
    array
    nulls
+   repeat
 
 Array Types
 -----------
 
+This function infers Arrow data type:
+
+.. autosummary::
+   :toctree: ../generated/
+
+   infer_type
+
 An array's Python class depends on its data type.  Concrete array classes
 may expose data type-specific methods or properties.
 
@@ -140,6 +149,8 @@ classes may expose data type-specific methods or properties.
    TimestampScalar
    DurationScalar
    MonthDayNanoIntervalScalar
+   Decimal32Scalar
+   Decimal64Scalar
    Decimal128Scalar
    Decimal256Scalar
    DictionaryScalar
diff --git a/docs/source/python/api/compute.rst b/docs/source/python/api/compute.rst
index 703eaf4ce5d..b74d674ac61 100644
--- a/docs/source/python/api/compute.rst
+++ b/docs/source/python/api/compute.rst
@@ -32,7 +32,11 @@ Aggregations
    approximate_median
    count
    count_distinct
+   first
+   first_last
    index
+   kurtosis
+   last
    max
    mean
    min
@@ -41,6 +45,7 @@ Aggregations
    pivot_wider
    product
    quantile
+   skew
    stddev
    sum
    tdigest
@@ -69,6 +74,7 @@ throws an ``ArrowInvalid`` exception when overflow is detected.
    cumulative_prod
    cumulative_prod_checked
    cumulative_max
+   cumulative_mean
    cumulative_min
 
 Arithmetic Functions
@@ -87,6 +93,8 @@ throws an ``ArrowInvalid`` exception when overflow is detected.
    add_checked
    divide
    divide_checked
+   exp
+   expm1
    multiply
    multiply_checked
    negate
@@ -126,6 +134,7 @@ representation based on the rounding criterion.
    ceil
    floor
    round
+   round_binary
    round_to_multiple
    trunc
 
@@ -171,6 +180,24 @@ variants which detect domain errors where appropriate.
    tan
    tan_checked
 
+Hyperbolic Trigonometric Functions
+----------------------------------
+
+Hyperbolic trigonometric functions are also supported, and, where applicable, also offer ``_checked``
+variants which detect domain errors if needed.
+
+.. autosummary::
+   :toctree: ../generated/
+
+   acosh
+   acosh_checked
+   asinh
+   atanh
+   atanh_checked
+   cosh
+   sinh
+   tanh
+
 Comparisons
 -----------
 
@@ -281,6 +308,7 @@ String Transforms
    utf8_capitalize
    utf8_length
    utf8_lower
+   utf8_normalize
    utf8_replace_slice
    utf8_reverse
    utf8_swapcase
@@ -338,6 +366,7 @@ String Component Extraction
    :toctree: ../generated/
 
    extract_regex
+   extract_regex_span
 
 String Joining
 --------------
@@ -425,10 +454,11 @@ Temporal Component Extraction
    day_of_week
    day_of_year
    hour
+   is_dst
+   is_leap_year
    iso_week
    iso_year
    iso_calendar
-   is_leap_year
    microsecond
    millisecond
    minute
@@ -472,12 +502,21 @@ Timezone Handling
    assume_timezone
    local_timestamp
 
+Random Number Generation
+------------------------
+
+.. autosummary::
+   :toctree: ../generated/
+
+   random
+
 Associative Transforms
 ----------------------
 
 .. autosummary::
    :toctree: ../generated/
 
+   dictionary_decode
    dictionary_encode
    unique
    value_counts
@@ -492,7 +531,9 @@ Selections
    array_take
    drop_null
    filter
+   inverse_permutation
    take
+   scatter
 
 Sorts and Partitions
 --------------------
@@ -501,9 +542,22 @@ Sorts and Partitions
    :toctree: ../generated/
 
    array_sort_indices
+   bottom_k_unstable
    partition_nth_indices
+   rank
+   rank_normal
+   rank_quantile
    select_k_unstable
    sort_indices
+   top_k_unstable
+
+Statistical Functions
+---------------------
+
+.. autosummary::
+   :toctree: ../generated/
+
+   winsorize
 
 Structural Transforms
 ---------------------
@@ -531,6 +585,7 @@ Pairwise Functions
    :toctree: ../generated/
 
    pairwise_diff
+   pairwise_diff_checked
 
 Compute Options
 ---------------
@@ -542,14 +597,17 @@ Compute Options
    AssumeTimezoneOptions
    CastOptions
    CountOptions
+   CumulativeOptions
    CumulativeSumOptions
    DayOfWeekOptions
    DictionaryEncodeOptions
    ElementWiseAggregateOptions
    ExtractRegexOptions
+   ExtractRegexSpanOptions
    FilterOptions
    IndexOptions
    JoinOptions
+   ListFlattenOptions
    ListSliceOptions
    MakeStructOptions
    MapLookupOptions
@@ -557,13 +615,16 @@ Compute Options
    ModeOptions
    NullOptions
    PadOptions
-   ZeroFillOptions
    PairwiseOptions
    PartitionNthOptions
    PivotWiderOptions
    QuantileOptions
+   RandomOptions
+   RankOptions
+   RankQuantileOptions
    ReplaceSliceOptions
    ReplaceSubstringOptions
+   RoundBinaryOptions
    RoundOptions
    RoundTemporalOptions
    RoundToMultipleOptions
@@ -571,6 +632,7 @@ Compute Options
    ScalarAggregateOptions
    SelectKOptions
    SetLookupOptions
+   SkewOptions
    SliceOptions
    SortOptions
    SplitOptions
@@ -581,8 +643,22 @@ Compute Options
    TakeOptions
    TDigestOptions
    TrimOptions
+   Utf8NormalizeOptions
    VarianceOptions
    WeekOptions
+   WinsorizeOptions
+   ZeroFillOptions
+
+Functions Registry
+------------------
+
+.. autosummary::
+   :toctree: ../generated/
+
+   call_function
+   call_tabular_function
+   get_function
+   list_functions
 
 User-Defined Functions
 ----------------------
@@ -590,7 +666,10 @@ User-Defined Functions
 .. autosummary::
    :toctree: ../generated/
 
+   register_aggregate_function
    register_scalar_function
+   register_tabular_function
+   register_vector_function
    UdfContext
 
 Expression Functions