Question: If this is my likelihood: $$ L(theta | text{data}) propto prod_{i=1}^{n} theta alpha^{theta} x_i^{-(theta+1)} $$ and the conjugate prior for theta is gamma distribution with

If this is my likelihood: $$ L(\theta | \text{data}) \propto \prod_{i=1}^{n} \theta \alpha^{\theta} x_i^{-(\theta+1)} $$ and the conjugate prior for theta is gamma distribution with parameter (a,b) can you help me calculate the posterior distribution for theta? which distribution does this posterior follows

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