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

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