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Rafael-SOWNet merged 1 commit into from
Oct 29, 2026
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The harmonic numbers #2200

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17 changes: 15 additions & 2 deletions BREAKING-CHANGES.md
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Expand Up @@ -483,7 +483,7 @@ the right shape, written out or once its operations are carried out, throws `Inv
**Not silent: these names followed by a bracket now throw `UnrecognizedFunctionParseException` where they were read as
products.** An unknown name followed by a bracket is a product, so `zeta(2)` was `zeta * 2` and simplified to
`2 * zeta`. The long names of the functions the library is to have are refused until each is implemented, as `trunc`
is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog`, `harmonicnumber` and
is: `zeta`, `riemannzeta`, `hurwitzzeta`, `lambertw`, `productlog` and
`forwarddifference`. Names that will not be functions,
because what they mean differs between sources or is already written exactly, are refused with the spelling to use:
`heaviside`, `unitstep`, `isprime`, `pochhammer`, `doublefactorial`, `factorial2`, `fractionalpart` and `quotient`.
Expand All @@ -496,7 +496,7 @@ Each name without a bracket is still a variable, and short names such as `beta`
| `"zeta(2)".ToEntity().Simplify()` | `2 * zeta` | throws `UnrecognizedFunctionParseException` |
| `"isprime(7)".ToEntity()` | `isprime * 7` | throws `UnrecognizedFunctionParseException`: write `n in PP` |
| `"heaviside(x)".ToEntity()` | `heaviside * x` | throws `UnrecognizedFunctionParseException`: write `iverson(x > 0)`, `iverson(x >= 0)` or `(1 + sgn(x))/2` |
| `"harmonicnumber(n, m)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` |
| `"hurwitzzeta(s, a)".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` |

### The Möbius, divisor and prime-counting functions

Expand Down Expand Up @@ -532,6 +532,19 @@ is ([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).
| `"hessian(x^3 y^2, [x, y])".ToEntity().Simplify()` | throws `UnhandledParseException` | `[[6 * x * y ^ 2, 6 * x ^ 2 * y], [6 * x ^ 2 * y, 2 * x ^ 3]]` |
| `"jacobian(x y, {x, y})".ToEntity()` | throws `UnhandledParseException` | throws `InvalidArgumentParseException`: a set has no order for the columns |

### The harmonic numbers

**Not silent: `harmonicnumber(n)` and `harmonicnumber(n, m)` are the harmonic numbers, where the one was a product and the
other a parse error.** They are `1 + 1/2^m + ... + 1/n^m` for a whole `n >= 0`, exact for a rational `m`, and
`ζ(m) - ζ(m, n + 1)` elsewhere, as Mathematica's `HarmonicNumber` is: `ψ(n + 1) - ψ(1)` for `m = 1`, evaluated numerically
through `digamma` and `polygamma` for a whole `m >= 1`. A negative integer `n` has no value but for a whole `m <= 0`
([#2182](https://github.com/asc-community/AngouriMath/issues/2182)).

| Input | Was (2.6.0) | Now |
|---|---|---|
| `"harmonicnumber(4)".ToEntity().Simplify()` | `4 * harmonicnumber` | `25/12` |
| `"harmonicnumber(n, 2)".ToEntity()` | throws `UnhandledParseException` | `harmonicnumber(n, 2)` |

### The Catalan numbers

**Not silent: `catalannumber(n)` is the Catalan number, where it was a product.** It is `binomial(2n, n) / (n + 1)` for
Expand Down
3 changes: 3 additions & 0 deletions Sources/.editorconfig
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Expand Up @@ -829,3 +829,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed

[Tests/UnitTests/Convenience/CatalanNumberTest.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/HarmonicNumberTest.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
8 changes: 8 additions & 0 deletions Sources/AngouriMath/Convenience/MathS.cs
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Expand Up @@ -1387,6 +1387,14 @@ public static Entity VectorLength(Matrix v)
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Entity Binomial(Entity n, Entity k) => new Binomialf(n, k);

/// <summary>The harmonic number <c>H_n = 1 + 1/2 + ... + 1/n</c></summary>
/// <remarks>https://github.com/asc-community/AngouriMath/issues/2182</remarks>
public static Entity HarmonicNumber(Entity n) => new HarmonicNumberf(n, Integer.One);

/// <summary>The generalized harmonic number <c>H_n^(m) = 1 + 1/2^m + ... + 1/n^m</c></summary>
/// <remarks>https://github.com/asc-community/AngouriMath/issues/2182</remarks>
public static Entity HarmonicNumber(Entity n, Entity m) => new HarmonicNumberf(n, m);

/// <summary>The Catalan number <c>C_n = binomial(2n, n) / (n + 1)</c></summary>
/// <remarks>https://github.com/asc-community/AngouriMath/issues/2182</remarks>
public static Entity CatalanNumber(Entity n) => new CatalanNumberf(n);
Expand Down
2 changes: 1 addition & 1 deletion Sources/AngouriMath/Core/Antlr/AngouriMath.g
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Expand Up @@ -627,6 +627,7 @@ atom returns[Entity value]
| 'binomial(' args = function_arguments ')' { Assert("binomial", 2, $args.list.Count); $value = MathS.Binomial($args.list[0], $args.list[1]); }
| 'multinomial(' args = function_arguments ')' { $value = ParsingHelpers.Multinomial($args.list); }
| 'catalannumber(' args = function_arguments ')' { Assert("catalannumber", 1, $args.list.Count); $value = MathS.CatalanNumber($args.list[0]); }
| 'harmonicnumber(' args = function_arguments ')' { if (Assert("harmonicnumber", (2, 1), $args.list.Count)) $value = MathS.HarmonicNumber($args.list[0], $args.list[1]); else $value = MathS.HarmonicNumber($args.list[0]); }
| 'fallingfactorial(' args = function_arguments ')' { Assert("fallingfactorial", 2, $args.list.Count); $value = MathS.FallingFactorial($args.list[0], $args.list[1]); }
| 'factorialpower(' args = function_arguments ')' { Assert("factorialpower", 2, $args.list.Count); $value = MathS.FallingFactorial($args.list[0], $args.list[1]); }
| 'risingfactorial(' args = function_arguments ')' { Assert("risingfactorial", 2, $args.list.Count); $value = MathS.RisingFactorial($args.list[0], $args.list[1]); }
Expand Down Expand Up @@ -695,7 +696,6 @@ atom returns[Entity value]
| 'hurwitzzeta(' args = function_arguments ')' { $value = NotImplementedFunction("hurwitzzeta", "Hurwitz zeta function yet"); }
| 'lambertw(' args = function_arguments ')' { $value = NotImplementedFunction("lambertw", "Lambert W function yet"); }
| 'productlog(' args = function_arguments ')' { $value = NotImplementedFunction("productlog", "Lambert W function yet"); }
| 'harmonicnumber(' args = function_arguments ')' { $value = NotImplementedFunction("harmonicnumber", "harmonic numbers yet"); }
| 'forwarddifference(' args = function_arguments ')' { $value = NotImplementedFunction("forwarddifference", "forward difference yet"); }
/* Names that will not be functions, refused with the spelling to use: what they mean is
ambiguous between sources, or is already written exactly another way. */
Expand Down
2 changes: 1 addition & 1 deletion Sources/AngouriMath/Core/Antlr/AngouriMath.interp
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Expand Up @@ -176,6 +176,7 @@ null
'binomial('
'multinomial('
'catalannumber('
'harmonicnumber('
'fallingfactorial('
'factorialpower('
'risingfactorial('
Expand Down Expand Up @@ -215,7 +216,6 @@ null
'hurwitzzeta('
'lambertw('
'productlog('
'harmonicnumber('
'forwarddifference('
'heaviside('
'unitstep('
Expand Down
80 changes: 40 additions & 40 deletions Sources/AngouriMath/Core/Antlr/AngouriMath.tokens
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Expand Up @@ -411,46 +411,46 @@ WS=237
'binomial('=174
'multinomial('=175
'catalannumber('=176
'fallingfactorial('=177
'factorialpower('=178
'risingfactorial('=179
'iverson('=180
'aleph('=181
'erf('=182
'erfc('=183
'erfi('=184
'Ei('=185
'li('=186
'polygamma('=187
'digamma('=188
'Si('=189
'Ci('=190
'Shi('=191
'Chi('=192
'det('=193
'transpose('=194
'dot('=195
'cross('=196
'laplacian('=197
'jacobian('=198
'hessian('=199
'resultant('=200
'conjugate('=201
'conj('=202
'arg('=203
'Re('=204
'Im('=205
're('=206
'real('=207
'im('=208
'imag('=209
'trunc('=210
'zeta('=211
'riemannzeta('=212
'hurwitzzeta('=213
'lambertw('=214
'productlog('=215
'harmonicnumber('=216
'harmonicnumber('=177
'fallingfactorial('=178
'factorialpower('=179
'risingfactorial('=180
'iverson('=181
'aleph('=182
'erf('=183
'erfc('=184
'erfi('=185
'Ei('=186
'li('=187
'polygamma('=188
'digamma('=189
'Si('=190
'Ci('=191
'Shi('=192
'Chi('=193
'det('=194
'transpose('=195
'dot('=196
'cross('=197
'laplacian('=198
'jacobian('=199
'hessian('=200
'resultant('=201
'conjugate('=202
'conj('=203
'arg('=204
'Re('=205
'Im('=206
're('=207
'real('=208
'im('=209
'imag('=210
'trunc('=211
'zeta('=212
'riemannzeta('=213
'hurwitzzeta('=214
'lambertw('=215
'productlog('=216
'forwarddifference('=217
'heaviside('=218
'unitstep('=219
Expand Down
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