Using the Mittag-Leffler function, show that: : e²=¹; a) E1,2(22) = 1; b) E2,1 (−2²) = cos(2); c) E2,2(-2²) = sin(2) Show that for the two-parameter Mittag-Leffler function, the following holds: Ea,8(2) + Ea,8(-2) = 2E2a,8(2²). Calculate the Laplace transform of the following Mittag-Leffler expressions: a) L{Ea(−λt)}; b) L{t³-¹ Ea,s(-λta)}.

Using the Mittag-Leffler function, show that: : e²=¹; a) E1,2(22) = 1; b) E2,1 (−2²) = cos(2); c) E2,2(-2²) = sin(2) Show that for the two-parameter Mittag-Leffler function, the following holds: Ea,8(2) + Ea,8(-2) = 2E2a,8(2²). Calculate the Laplace transform of the following Mittag-Leffler expressions: a) L{Ea(−λt)}; b) L{t³-¹ Ea,s(-λta)}.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 50E

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