On some expansions for the Euler Gamma function and the Riemann Zeta function

Rza̧dkowski, Grzegorz

doi:10.1016/j.cam.2011.08.020

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-Variable Truncated1

Expansion In Derivatives1

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Cited by 6 publications

(2 citation statements)

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“…Recent developments related to Mittag-Leffler polynomials and their generalizations are considered in [12,17]. An application of the Mittag-Leffler polynomials to an expansion for the Riemann zeta function is discussed in [15].…”

Section: -Variable Truncatedmentioning

confidence: 99%

Operational Methods and Truncated Exponential-Based Mittag-Leffler Polynomials

2015

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Section: -Variable Truncatedmentioning

confidence: 99%

Operational Methods and Truncated Exponential-Based Mittag-Leffler Polynomials

2015

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“…For the gamma subordinator, the constants

a_{n}

simplify to

a_{n} = n!

, so

c_{m, j} = \frac{1}{m!} Y_{m, j} (\frac{1!}{2}, \frac{2!}{3}, \frac{3!}{4}, ...) .

We can calculate the

c_{m, j}

efficiently via recurrence. Rz

a ̧

dkowski () shows that

c_{m, j} = \frac{1}{m + j} (c_{m - 1, j - 1} + (m + j - 1) c_{m - 1, j})

…”

Section: Expansion In Derivativesmentioning

confidence: 99%

Expectations of Functions of Stochastic Time With Application to Credit Risk Modeling

Costin

Gordy

Huang

et al. 2014

Mathematical Finance

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We develop two novel approaches to solving for the Laplace transform of a time-changed stochastic process. We discard the standard assumption that the background process (X t ) is Lévy. Maintaining the assumption that the business clock (T t ) and the background process are independent, we develop two different series solutions for the Laplace transform of the time-changed processX t = X(T t ). In fact, our methods apply not only to Laplace transforms, but more generically to expectations of smooth functions of random time. We apply the methods to introduce stochastic time change to the standard class of default intensity models of credit risk, and show that stochastic time-change has a very large effect on the pricing of deep out-of-the-money options on credit default swaps.JEL Codes: G12, G13

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