(11) Consider the Gelfand-Shilov function given by: if x > 0, Φλ (2) 10° if x ≤0. with Re(A) > 0. Show that a(z) * 03(x) = 0α+3(x). (12) Show that given the functions f(t) = t−1 and g(t) = t2-1, it holds that f(t)g(t) = +4-1B(p,q). (13) Using the Mittag-Leffler function, show that: a) E1,2(2²) = -1; b) E2.1(-z²) = cos(2); c) E2.2 (-2²) sin() = (14) Show that for the two-parameter Mittag-Leffler function, the following holds: Ea.(2) + Ea.(-2) = 2Еas (2²). (15) Compute the Laplace transform of the following Mittag-Leffler expressions: a) L{E(-λt)}; b) L{tª¹E₁(−λtº)}.
(11) Consider the Gelfand-Shilov function given by: if x > 0, Φλ (2) 10° if x ≤0. with Re(A) > 0. Show that a(z) * 03(x) = 0α+3(x). (12) Show that given the functions f(t) = t−1 and g(t) = t2-1, it holds that f(t)g(t) = +4-1B(p,q). (13) Using the Mittag-Leffler function, show that: a) E1,2(2²) = -1; b) E2.1(-z²) = cos(2); c) E2.2 (-2²) sin() = (14) Show that for the two-parameter Mittag-Leffler function, the following holds: Ea.(2) + Ea.(-2) = 2Еas (2²). (15) Compute the Laplace transform of the following Mittag-Leffler expressions: a) L{E(-λt)}; b) L{tª¹E₁(−λtº)}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please
Transcribed Image Text:(11) Consider the Gelfand-Shilov function given by:
if x > 0,
Φλ (2)
10°
if x ≤0.
with Re(A) > 0. Show that a(z) * 03(x) = 0α+3(x).
(12) Show that given the functions f(t) = t−1 and g(t) = t2-1, it holds that
f(t)g(t) =
+4-1B(p,q).
(13) Using the Mittag-Leffler function, show that:
a) E1,2(2²) = -1;
b) E2.1(-z²) = cos(2);
c) E2.2 (-2²)
sin()
=
(14) Show that for the two-parameter Mittag-Leffler function, the following holds:
Ea.(2) + Ea.(-2) = 2Еas (2²).
(15) Compute the Laplace transform of the following Mittag-Leffler expressions:
a) L{E(-λt)};
b) L{tª¹E₁(−λtº)}.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
