Formula:839

Digital Library of Mathematical Functions ID 2.6.E43

${\displaystyle{\displaystyle t^{\mu-1}\ast f=\sum_{s=0}^{n-1}a_{s}\frac{\Gamma\left(\mu\right)\Gamma\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}t^{\mu-s-\alpha}-\sum_{s=1}^{n}c_{s}\frac{\Gamma\left(\mu\right)}{\Gamma\left(\mu-s+1\right)}t^{\mu-s}+t^{\mu-1}\ast f_{n}}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mu}}$: order
• ${\displaystyle{\displaystyle\ast}}$: convolution (locally)
• ${\displaystyle{\displaystyle f(t)}}$: locally integrable function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle a_{n}}}$: coefficients
• ${\displaystyle{\displaystyle f_{n,n}(t)}}$: n th repeated integral
• ${\displaystyle{\displaystyle c_{s}}}$: real
 

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