Let us consider the two functions $$F(x) = \int\limits_x^1 {h(s - x,s)ds - } \int\limits_{1 - x}^1 {h(2 - s - x,s)ds} $$$$G(x) = \int\limits_0^x {h(x - s,s)ds - } \int\limits_0^{1 - x} {h(x + s,s)ds} $$ Where $h$ is some regular function. Note that $F(0)=-G(0)$, and $F(1)=-G(1)$. But I can not find a general relation between these two functions. I will be grateful to yiur helps. Thank you.

  • $\begingroup$ Could you share your thoughts, why you think there should be a general relation linking the two functions directly? $\endgroup$ – maxmilgram Jan 11 at 12:03
  • $\begingroup$ I have some intuition about that by I'm not sure. I've made many of variable substation but I didn't succeed. $\endgroup$ – Gustave Jan 11 at 12:05

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.