# Numerical integration gives errors NIntegrate::slwcon: and Integrate::eincr:

I have a problem with numerical integration of this function:

function =
(Cos[kx] (6/5 + 2 Cos[kz]) +  2 Cos[kz] (6/5 + (I Sin[kx])/Sqrt[2])) /
((496/25 + (48 Cos[kz])/5 +  48/5 Cos[kx] (2 + (6 Cos[kz])/5) -
36/25 Cos[2 kz] +  48/5 I Sqrt[2] Sin[kx])^(3/2));

NIntegrate[function, {kx, 0, 2 π}, {kz, 0, 2 π},
Exclusions -> (Denominator[function] == 0),
MinRecursion -> 2,
MaxRecursion -> 100,
AccuracyGoal -> 10,
PrecisionGoal -> 10,
MaxPoints -> 500000,
WorkingPrecision -> 30]


it gives me this error:

NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small.

NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained 0.53526925420640569943007319700700198085548160409944705790923206744819749466536515-7.2044646992384345994673912539292596550305823592711091867857439782901606888780460*10^-8 I and 0.0001094833119173794600994710770298010369210430029834317124615138828472025457359260180. for the integral and error estimates.

So is there a more efficient solution to my problem?

• Your code does not evaluate. Please give the missing definitions of m, t, and γ`. – m_goldberg Aug 29 '18 at 13:32
• Hi, the integration has been revised. Thanks. – Steven Aug 30 '18 at 0:20
• Why do you think the integral converges? It seems to have singularities that cause the integral to blow up. – Carl Woll Aug 30 '18 at 1:47