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For $t=i$ there is a formula involving an integral of a Bessel function, so I doubt there is a simple closed formula for $K_{\alpha}$ in general. You can find the formula I mentioned in the first page of the article "Some theorems on stable processes" by Blumenthal and Getoor. Also see this related MO questionthis related MO question.

For $t=i$ there is a formula involving an integral of a Bessel function, so I doubt there is a simple closed formula for $K_{\alpha}$ in general. You can find the formula I mentioned in the first page of the article "Some theorems on stable processes" by Blumenthal and Getoor. Also see this related MO question.

For $t=i$ there is a formula involving an integral of a Bessel function, so I doubt there is a simple closed formula for $K_{\alpha}$ in general. You can find the formula I mentioned in the first page of the article "Some theorems on stable processes" by Blumenthal and Getoor. Also see this related MO question.

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Abdelmalek Abdesselam
Abdelmalek Abdesselam
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For $t=i$ there is a formula involving andan integral of a Bessel function, so I doubt there is a simple closed formula for $K_{\alpha}$ in general. You can find the formula I mentioned in the first page of the article "Some theorems on stable processes" by Blumenthal and Getoor. Also see this related MO question.

For $t=i$ there is a formula involving and integral of a Bessel function, so I doubt there is a simple closed formula for $K_{\alpha}$ in general. You can find the formula I mentioned in the first page of the article "Some theorems on stable processes" by Blumenthal and Getoor. Also see this related MO question.

For $t=i$ there is a formula involving an integral of a Bessel function, so I doubt there is a simple closed formula for $K_{\alpha}$ in general. You can find the formula I mentioned in the first page of the article "Some theorems on stable processes" by Blumenthal and Getoor. Also see this related MO question.

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Abdelmalek Abdesselam
Abdelmalek Abdesselam
  • 23k
  • 1
  • 67
  • 127

For $t=i$ there is a formula involving and integral of a Bessel function, so I doubt there is a simple closed formula for $K_{\alpha}$ in general. You can find the formula I mentioned in the first page of the article "Some theorems on stable processes" by Blumenthal and Getoor. Also see this related MO question.