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Results tagged with cv.complex-variables
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user 143419
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
- 113
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 $$\frac{\partial^{m+n}}{\partial y^m \partial x^n} f …
- 113
5
votes
2
answers
763
views
How to calculate an integral over the complex unit sphere
We want to calculate the following integral over the complex unit sphere $S^{2n-1}$:
$$\int_{S^{2n-1}} \frac{1 }{|1 - \langle z, \zeta \rangle|^2} \, d\sigma(\zeta),$$
where $ z $ is a fixed point in …
- 113