1
$\begingroup$

Is the following equation true for Tricomi confluent Hypergeometric function? $$\phi(1,0,ax)=1-ax\phi(1,1,ax)$$ here $\phi(.,.,.)$ is the Tricomi confluent hypergeometric function. Thanks in advance.

$\endgroup$
  • $\begingroup$ I think that using the gamma function could help. $\endgroup$ – Claude Leibovici Nov 7 '16 at 13:59
1
$\begingroup$

As usual examine carefully :)
Using DLMF 13.2.11, 13.6.6
$U(1,0,z)=z\cdot U\left(2,2,z\right)=e^{z}\cdot E_{2}\left(z\right)$
$z\cdot U(1,1,z)=z\cdot e^{z}E_{1}\left(z\right)$
So your question is
$E_{2}\left(z\right)+z\cdot E_{1}\left(z\right)=e^{-z}$
Which matches 8.19.12

$\endgroup$
  • $\begingroup$ Thanks alot for your answer. I checked and my equation exactly matches according to 8.19.12 $\endgroup$ – Frank Moses Nov 8 '16 at 23:52
  • $\begingroup$ Tsk..tsk.. Thanks for giving me a chance to fix mine. $\endgroup$ – rrogers Nov 9 '16 at 15:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.