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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

-2 votes
0 answers
113 views

How to calculate this integral [closed]

Is there a formula of this integral $$\int_{S_{2n-1}} \frac{e^{i a \langle z, \zeta \rangle}}{|z - \zeta|^{2\lambda}} \, d\sigma(\zeta)$$ and how to calculate it. Thank you in advance
0 votes
0 answers
35 views

Derivate involving Bessel function of second type

Let. $$f := (x, y) \mapsto \text{BesselK}(1, c \cdot (a - b \cdot (x + y))) \cdot \exp(c \cdot b \cdot (y - x))$$ Is there a close formula for this $$\frac{\partial^{m+n}}{\partial y^m \partial x^n} f …
5 votes
2 answers
763 views

How to calculate an integral over the complex unit sphere

We want to calculate the following integral over the complex unit sphere $S^{2n-1}$: $$\int_{S^{2n-1}} \frac{1 }{|1 - \langle z, \zeta \rangle|^2} \, d\sigma(\zeta),$$ where $ z $ is a fixed point in …