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+## Copyright 2021 Ian Jauslin
+## 
+## Licensed under the Apache License, Version 2.0 (the "License");
+## you may not use this file except in compliance with the License.
+## You may obtain a copy of the License at
+## 
+##     http://www.apache.org/licenses/LICENSE-2.0
+## 
+## Unless required by applicable law or agreed to in writing, software
+## distributed under the License is distributed on an "AS IS" BASIS,
+## WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+## See the License for the specific language governing permissions and
+## limitations under the License.
+
+# approximate \int_a^b f using Gauss-Legendre quadratures
+@everywhere function integrate_legendre(f,a,b,weights)
+  out=0
+  for i in 1:length(weights[1])
+    out+=(b-a)/2*weights[2][i]*f((b-a)/2*weights[1][i]+(b+a)/2)
+  end
+  return out
+end
+# \int f*g where g is sampled at the Legendre nodes
+@everywhere function integrate_legendre_sampled(f,g,a,b,weights)
+  out=0
+  for i in 1:length(weights[1])
+    out+=(b-a)/2*weights[2][i]*f((b-a)/2*weights[1][i]+(b+a)/2)*g[i]
+  end
+  return out
+end
+
+
+# approximate \int_a^b f/sqrt((b-x)(x-a)) using Gauss-Chebyshev quadratures
+@everywhere function integrate_chebyshev(f,a,b,N)
+  out=0
+  for i in 1:N
+    out=out+pi/N*f((b-a)/2*cos((2*i-1)/(2*N)*pi)+(b+a)/2)
+  end
+  return out
+end
+
+# approximate \int_0^\infty dr f(r)*exp(-a*r) using Gauss-Chebyshev quadratures
+@everywhere function integrate_laguerre(f,a,weights_gL)
+  out=0.
+  for i in 1:length(weights_gL[1])
+    out+=1/a*f(weights_gL[1][i]/a)*weights_gL[2][i]
+  end
+  return out
+end
+
+# Hann window
+@everywhere function hann(x,L)
+  if abs(x)<L/2
+    return cos(pi*x/L)^2
+  else
+    return 0.
+  end
+end