What is inverse Laplace of following function? F(s)=L^(-1) ((Gamma(−s/a+b+1/4))/(Gamma(1/4−s/a)))

manudyent7 2022-09-17 Answered
What is inverse Laplace of following function?
F ( s ) = L 1 ( Γ ( s a + b + 1 4 ) Γ ( 1 4 s a ) )
You can still ask an expert for help

Want to know more about Laplace transform?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

rougertl
Answered 2022-09-18 Author has 16 answers
The ratio of the gamma functions grows as s b , therefore we need b < 0 in order for the Bromwich integral to be convergent. Further, we need all poles to lie to the left of a vertical line, which is possible if either a < 0 or b Z . In the latter case the poles in the numerator and in the denominator cancel out. With these assumptions,
L 1 [ Γ ( s a + b + 1 4 ) Γ ( s a + 1 4 ) ] = a e a t ( b + 1 / 4 ) k 0 ( 1 ) k + 1 e a t k Γ ( k b ) k ! = a e a t ( b + 1 / 4 ) Γ ( b ) k 0 ( 1 ) k ( b 1 k ) e a t k = a e a t ( b + 1 / 4 ) Γ ( b ) ( 1 e a t ) b 1 .

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions