From 399301c9f9c5bb801af389d50ca7dc2adbd562b3 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Sun, 20 Apr 2025 00:58:53 -0300
Subject: Added singular solution

---
 log-fourier_integrator.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/log-fourier_integrator.cpp b/log-fourier_integrator.cpp
index 51f5326..b21f275 100644
--- a/log-fourier_integrator.cpp
+++ b/log-fourier_integrator.cpp
@@ -76,10 +76,10 @@ int main(int argc, char* argv[]) {
 
   /* Start from the exact solution for β = 0 */
   for (unsigned n = 0; n < N; n++) {
-    if (τ₀ > 0) {
+    if (τ₀ != 1) {
       Cₜ₋₁[n] = Γ₀ * (exp(-μ * fft.t(n)) - μ * τ₀ * exp(-fft.t(n) / τ₀)) / (μ - pow(μ, 3) * pow(τ₀, 2));
     } else {
-      Cₜ₋₁[n] = Γ₀ * exp(-μ * fft.t(n)) / μ;
+      Cₜ₋₁[n] = Γ₀ * exp(-fft.t(n)) * (1 + fft.t(n));
     }
     Rₜ₋₁[n] = exp(-μ * fft.t(n));
 
-- 
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