diff --git a/crates/dekoder/src/eko.rs b/crates/dekoder/src/eko.rs
index 1df9d7811..50112e352 100644
--- a/crates/dekoder/src/eko.rs
+++ b/crates/dekoder/src/eko.rs
@@ -92,7 +92,7 @@ impl EKO {
     pub fn write(&self, dst: PathBuf) -> Result<()> {
         self.assert_working_dir()?;
         // create writer
-        let dst_file = File::create(&dst)?;
+        let dst_file = File::create(dst)?;
         let dst_file = BufWriter::with_capacity(TAR_WRITER_CAPACITY, dst_file);
         let mut ar = tar::Builder::new(dst_file);
         // do it!
@@ -101,7 +101,7 @@ impl EKO {
 
     /// Extract tar file from `src` to `dst`.
     pub fn extract(src: PathBuf, dst: PathBuf) -> Result<Self> {
-        let mut ar = tar::Archive::new(File::open(&src)?);
+        let mut ar = tar::Archive::new(File::open(src)?);
         ar.unpack(&dst)?;
         Self::load_opened(dst)
     }
diff --git a/crates/ekore/src/harmonics/cache.rs b/crates/ekore/src/harmonics/cache.rs
index b15ba4dcc..89ae8f3e0 100644
--- a/crates/ekore/src/harmonics/cache.rs
+++ b/crates/ekore/src/harmonics/cache.rs
@@ -30,10 +30,18 @@ pub enum K {
     S3mh,
     /// $g_3(N)$
     G3,
+    /// $S_{-1}(N)$ even moments
+    Sm1e,
+    /// $S_{-1}(N)$ odd moments
+    Sm1o,
     /// $S_{-2}(N)$ even moments
     Sm2e,
     /// $S_{-2}(N)$ odd moments
     Sm2o,
+    /// $S_{-2,1}(N)$ even moments
+    Sm21e,
+    /// $S_{-2,1}(N)$ odd moments
+    Sm21o,
 }
 
 /// Hold all cached values.
@@ -78,8 +86,12 @@ impl Cache {
             K::S2mh => w2::S2((self.n - 1.) / 2.),
             K::S3mh => w3::S3((self.n - 1.) / 2.),
             K::G3 => g_functions::g3(self.n, self.get(K::S1)),
+            K::Sm1e => w1::Sm1e(self.get(K::S1), self.get(K::S1h)),
+            K::Sm1o => w1::Sm1o(self.get(K::S1), self.get(K::S1mh)),
             K::Sm2e => w2::Sm2e(self.get(K::S2), self.get(K::S2h)),
             K::Sm2o => w2::Sm2o(self.get(K::S2), self.get(K::S2mh)),
+            K::Sm21e => w3::Sm21e(self.n, self.get(K::S1), self.get(K::Sm1e)),
+            K::Sm21o => w3::Sm21o(self.n, self.get(K::S1), self.get(K::Sm1o)),
         };
         // insert
         self.m.insert(k, val);
diff --git a/crates/ekore/src/harmonics/w1.rs b/crates/ekore/src/harmonics/w1.rs
index a1aa893d9..64431e6d0 100644
--- a/crates/ekore/src/harmonics/w1.rs
+++ b/crates/ekore/src/harmonics/w1.rs
@@ -10,3 +10,13 @@ use crate::harmonics::polygamma::cern_polygamma;
 pub fn S1(N: Complex<f64>) -> Complex<f64> {
     cern_polygamma(N + 1.0, 0) + 0.577_215_664_901_532_9
 }
+
+/// Analytic continuation of harmonic sum $S_{-1}(N)$ for even moments.
+pub fn Sm1e(hS1: Complex<f64>, hS1h: Complex<f64>) -> Complex<f64> {
+    hS1h - hS1
+}
+
+/// Analytic continuation of harmonic sum $S_{-1}(N)$ for odd moments.
+pub fn Sm1o(hS1: Complex<f64>, hS1mh: Complex<f64>) -> Complex<f64> {
+    hS1mh - hS1
+}
diff --git a/crates/ekore/src/harmonics/w3.rs b/crates/ekore/src/harmonics/w3.rs
index 7850c678d..2987db7ff 100644
--- a/crates/ekore/src/harmonics/w3.rs
+++ b/crates/ekore/src/harmonics/w3.rs
@@ -1,7 +1,9 @@
 //! Harmonic sums of weight 3.
 use num::complex::Complex;
+use std::f64::consts::LN_2;
 
-use crate::constants::ZETA3;
+use crate::constants::{ZETA2, ZETA3};
+use crate::harmonics::g_functions::g3;
 use crate::harmonics::polygamma::cern_polygamma;
 
 /// Compute the harmonic sum $S_3(N)$.
@@ -11,3 +13,15 @@ use crate::harmonics::polygamma::cern_polygamma;
 pub fn S3(N: Complex<f64>) -> Complex<f64> {
     0.5 * cern_polygamma(N + 1.0, 2) + ZETA3
 }
+
+/// Analytic continuation of harmonic sum $S_{-2,1}(N)$ for even moments.
+pub fn Sm21e(N: Complex<f64>, hS1: Complex<f64>, hSm1: Complex<f64>) -> Complex<f64> {
+    let eta = 1.;
+    -eta * g3(N + 1., hS1 + 1. / (N + 1.)) + ZETA2 * hSm1 - 5. / 8. * ZETA3 + ZETA2 * LN_2
+}
+
+/// Analytic continuation of harmonic sum $S_{-2,1}(N)$ for odd moments.
+pub fn Sm21o(N: Complex<f64>, hS1: Complex<f64>, hSm1: Complex<f64>) -> Complex<f64> {
+    let eta = -1.;
+    -eta * g3(N + 1., hS1 + 1. / (N + 1.)) + ZETA2 * hSm1 - 5. / 8. * ZETA3 + ZETA2 * LN_2
+}