Better complex Gudermannian

paulmasson · Jun 16, 2021 · 5559263 · 5559263
1 parent d10305b
commit 5559263
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Showing 2 changed files with 10 additions and 4 deletions.
diff --git a/build/math.js b/build/math.js
@@ -3674,9 +3674,12 @@ function sinc( x ) {
 
 }
 
-function gudermannian( x ) { return arctan( sinh(x) ); }
 
-function inverseGudermannian( x ) { return arctanh( sin(x) ); }
+// analyticphysics.com / The Complex Gudermannian Function
+
+function gudermannian( x ) { return mul( 2, arctan( tanh( div(x,2) ) ) ); }
+
+function inverseGudermannian( x ) { return mul( 2, arctanh( tan( div(x,2) ) ) ); }
 
 
 function zeta( x, tolerance=1e-10 ) {

diff --git a/src/functions/trigonometry.js b/src/functions/trigonometry.js
@@ -359,7 +359,10 @@ function sinc( x ) {
 
 }
 
-function gudermannian( x ) { return arctan( sinh(x) ); }
 
-function inverseGudermannian( x ) { return arctanh( sin(x) ); }
+// analyticphysics.com / The Complex Gudermannian Function
+
+function gudermannian( x ) { return mul( 2, arctan( tanh( div(x,2) ) ) ); }
+
+function inverseGudermannian( x ) { return mul( 2, arctanh( tan( div(x,2) ) ) ); }