The double factorial is the postfix n!!

BREAKING-CHANGES.md

@@ -290,6 +290,21 @@ the expression's own domain as its condition ([#2142](https://github.com/asc-com
 | `"(1 - cos(a))/(1 + cos(a))/tan(a/2)^2".Simplify()` | `(1 - cos(a)) / ((cos(a) + 1) * tan(a / 2) ^ 2)` | `1 provided not cos(a) + 1 = 0 and not tan(a / 2) = 0 and not cos(a / 2) = 0` |
 | `"(cos(2*x) - 1)^2 + sin(2*x)^2 - 4*sin(x)^2".Simplify()` ([#2133](https://github.com/asc-community/AngouriMath/issues/2133)) | `2 + (-2) * cos(2 * x) + (-4) * sin(x) ^ 2` | `0` |
 
+### The double factorial is the postfix `n!!`
+
+**Not silent: `n!!` is now the double factorial, where it was a parse error.** It is the product of the positive integers
+up to `n` with its parity, `0!!` and `(-1)!!` being `1`, and below them `n!! = (n + 2)!!/(n + 2)`. It has no value at a
+negative even integer or off the integers, since the extension through the gamma function does not give `0!! = 1`.
+`(n!)!` keeps its parentheses, and `n!!!`, the triple factorial, is refused rather than read as `(n!!)!`
+([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).
+
+| Input | Was (2.6.0) | Now |
+|---|---|---|
+| `"7!!".ToEntity().Simplify()` | throws `UnhandledParseException` | `105` |
+| `"(-5)!!".ToEntity().Simplify()` | throws `UnhandledParseException` | `1/3` |
+| `"n!!".ToEntity()` | throws `UnhandledParseException` | `n!!` |
+| `"n!!!".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` |
+
 ### `re` and `im` are the real and the imaginary part
 
 **Not silent: `re(…)` and `im(…)`, and `real(…)` and `imag(…)`, are now the real and the imaginary part, where they were

Sources/.editorconfig

@@ -246,6 +246,9 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
 [Tests/UnitTests/Convenience/RealAndImaginaryPartTest.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 
+[Tests/UnitTests/Convenience/DoubleFactorialTest.cs]
+file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
+
 [Tests/UnitTests/Convenience/IversonTest.cs]
 file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
 

Sources/AngouriMath/Convenience/MathS.cs

@@ -1484,6 +1484,33 @@ public static Entity VectorLength(Matrix v)
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
         public static Entity Im(Entity z) => new Imf(z);
 
+        /// <summary>The double factorial <c>n!!</c>: <c>n (n - 2) (n - 4) ...</c> down to 1 or 2</summary>
+        /// <param name="n">An integer, other than a negative even one</param>
+        /// <returns>The <see cref="Entity.DoubleFactorialf"/> node</returns>
+        /// <remarks>
+        /// <c>0!!</c> and <c>(-1)!!</c> are <c>1</c>, a negative odd <c>n</c> follows from
+        /// <c>n!! = (n + 2)!!/(n + 2)</c>, and off the integers it has no value. It is not <c>(n!)!</c>.
+        /// https://github.com/asc-community/AngouriMath/issues/2182
+        /// </remarks>
+        /// <example>
+        /// <code>
+        /// using System;
+        /// using static AngouriMath.MathS;
+        ///
+        /// Console.WriteLine(DoubleFactorial(7).Simplify());
+        /// Console.WriteLine(DoubleFactorial(8).Simplify());
+        /// Console.WriteLine(DoubleFactorial(-5).Simplify());
+        /// </code>
+        /// Prints
+        /// <code>
+        /// 105
+        /// 384
+        /// 1/3
+        /// </code>
+        /// </example>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Entity DoubleFactorial(Entity n) => new DoubleFactorialf(n);
+
         /// <summary>The aleph number <c>aleph(k)</c>, the size of an infinite set</summary>
         /// <param name="index">The index, a whole number from zero</param>
         /// <returns>The <see cref="Entity.Alephf"/> node</returns>

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -82,6 +82,11 @@ options
 // atom is defined later
 factorial_expression returns[Entity value]
     : p = atom '!' { $value = MathS.Factorial($p.value); }
+    /* The double factorial, n (n - 2) (n - 4) ..., which is not (n!)!: that keeps its parentheses.
+       Three marks are the triple factorial in the literature, which the library does not have, so
+       they are refused rather than read as (n!!)!. https://github.com/asc-community/AngouriMath/issues/2182 */
+    | p = atom '!!' { $value = MathS.DoubleFactorial($p.value); }
+    | p = atom '!!!' { throw new UnrecognizedFunctionParseException("n!!! is the triple factorial, which AngouriMath does not have; write (n!!)! for the factorial of a double factorial"); }
     | p = atom { $value = $p.value; }
     ;
 
@@ -698,8 +703,8 @@ atom returns[Entity value]
     | 'unitstep(' args = function_arguments ')' { $value = NotAFunctionHere("unitstep", "write iverson(x >= 0), which is 1 at 0"); }
     | 'isprime(' args = function_arguments ')' { $value = NotAFunctionHere("isprime", "write n in PP"); }
     | 'pochhammer(' args = function_arguments ')' { $value = NotAFunctionHere("pochhammer", "(x)_n is the rising factorial to some and the falling one to others; write risingfactorial or fallingfactorial"); }
-    | 'doublefactorial(' args = function_arguments ')' { $value = NotAFunctionHere("doublefactorial", "the double factorial is to be the postfix n!!, which is not implemented yet"); }
-    | 'factorial2(' args = function_arguments ')' { $value = NotAFunctionHere("factorial2", "the double factorial is to be the postfix n!!, which is not implemented yet"); }
+    | 'doublefactorial(' args = function_arguments ')' { $value = NotAFunctionHere("doublefactorial", "the double factorial is the postfix n!!"); }
+    | 'factorial2(' args = function_arguments ')' { $value = NotAFunctionHere("factorial2", "the double factorial is the postfix n!!"); }
     | 'fractionalpart(' args = function_arguments ')' { $value = NotAFunctionHere("fractionalpart", "write x mod 1, which is in [0, 1)"); }
     | 'quotient(' args = function_arguments ')' { $value = NotAFunctionHere("quotient", "write floor(a / b)"); }
     | 'domain(' args = function_arguments ')'