Add Riemann xi function

paulmasson · Sep 10, 2023 · 5b88ad5 · 5b88ad5
1 parent 931ee02
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diff --git a/build/math.js b/build/math.js
@@ -4411,6 +4411,14 @@ function zeta( x, tolerance=1e-10 ) {
 
 function dirichletEta( x ) { return mul( zeta(x), sub( 1, pow( 2, sub(1,x) ) ) ); }
 
+function riemannXi( x ) {
+
+  var half = div( x, 2 );
+
+  return mul( half, sub(x,1), pow( pi, neg(half) ), gamma(half), zeta(x) );
+
+}
+
 
 function bernoulli( n, x ) {
 

diff --git a/docs/functions.html b/docs/functions.html
@@ -335,6 +335,8 @@ <h1>Zeta Functions</h1>
 
 <p><a href="functions/dirichletEta.html"><b>dirichletEta( <i>x</i> )</b></a> &mdash; Dirichlet eta function of a real or complex number</p>
 
+<p><b>riemannXi( <i>n</i> )</b> &mdash; Riemman xi function of a real or complex number</p>
+
 <p><b>bernoulli( <i>n</i> )</b> &mdash; Bernoulli number for index <i>n</i>. Returns a generalized value for fractional, negative or complex indices.</p>
 
 <p><b>bernoulli( <i>n</i>, <i>x</i> )</b> &mdash; Bernoulli polynomial for real or complex index <i>n</i> of a real or complex number</p>

diff --git a/src/functions/zeta.js b/src/functions/zeta.js
@@ -76,6 +76,14 @@ function zeta( x, tolerance=1e-10 ) {
 
 function dirichletEta( x ) { return mul( zeta(x), sub( 1, pow( 2, sub(1,x) ) ) ); }
 
+function riemannXi( x ) {
+
+  var half = div( x, 2 );
+
+  return mul( half, sub(x,1), pow( pi, neg(half) ), gamma(half), zeta(x) );
+
+}
+
 
 function bernoulli( n, x ) {