Another "existence problem" in maths

Discussion in 'Physics & Math' started by Secret, Jul 24, 2014.

  1. Secret Registered Senior Member

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    http://www.phengkimving.com/calc_of...l/11_03_tests_for_conv_of_improper_intgrl.htm

    pics
    View attachment 7236

    Ok the question is
    he said that if we cannot find g(x) or h(x) such that the conditions specified there is obeyed, then the standard comparison test will not work
    Is there exist any method (similar to how one can show and prove that some integrals cannot be expressed as elementary functions) that can tell us that such g or h exist/do not exist even in principle, despite we might not be able to came up with it immediately probably because the g,h is a complicated expression?
     

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