Reflection of regular functions

It is proved in article, that a function with reflection in relation to some point can be the double reflection of initial function in relation to some other points. The double reflection results in the periodicity of some analytical function. In a example we obtain a periodic odd function, if we move the result of two reflections. We obtain a similar result after consideration of the 𝐹(𝑝) field: 𝐹(𝑝) = 𝑓(𝑝 - 2𝐴), if = + 𝑖𝑦, = 𝐴, for all 𝐴. The 𝐹(𝐴 + + 𝑖𝑦) values equal to the 𝑓(𝑧 - 2𝐴 - 2𝐵) values in the + + point as a result of two moving of the 𝑓(𝑝) function to the right for all (at first we move the 𝑓(-𝐴+𝑖𝑦) on the 2𝐴 distance, after we move the the 𝐹(𝑝) = 𝑓(𝐴+𝑖𝑦) = 𝑓(𝑝) function on the 2𝐵 distance in relation to center in the (𝐴, 0) point); the result of the such double moving is equal to the values of initial field in the 𝐴+𝐵 +𝑖𝑦 point. The reflection of the 𝐹(𝑝) field in the (𝐴, 0) and (𝐴 + 𝐵, 0) points is the 𝑓(-𝑝) regular function for all real 𝐴, 𝐵. We can move the 𝐹(𝑝) values in reverse direction (to the left). In the situation the values (in the left part of plane) are equal to the values of initial regular 𝑓(𝑝) function. As a result of two moving we obtain a new 𝐺(𝑝) field in relation to the 𝑓(𝑝) function after the movements to the left with the (-𝐴, 0) center. The regular 𝑓(𝑝) function is equal to the 𝐺(𝑝) field, if function show_eabstract() { $('#eabstract1').hide(); $('#eabstract2').show(); $('#eabstract_expand').hide(); }