Finding discrete solutions to inequality involving Exponential Integral
$begingroup$
I want to identify the least natural number $n$ (of course, it suffices to solve this problem for the reals, and then take the floor) such that
$$-c text{Ei}left(-e^{frac{a-d}{c}} (n+1)right)+a-b (n+1)+c log (n+1)+gamma c < 0,$$
where $text{Ei}$ is the exponential integral, $a,b, c, d$ are arbitrary real constants, and $gamma$ is the Euler-Mascheroni constant.
I have tried moving the terms around etc., to no avail; Mathematica also does not seem able to solve this.
I was wondering if there are any easy ways to solve this, or at least simplify it?
inequality optimization integral-inequality discrete-optimization functional-inequalities
asked Jan 1 at 16:45
jackson5jackson5
618513
$endgroup$
add a comment |
$begingroup$
I want to identify the least natural number $n$ (of course, it suffices to solve this problem for the reals, and then take the floor) such that
$$-c text{Ei}left(-e^{frac{a-d}{c}} (n+1)right)+a-b (n+1)+c log (n+1)+gamma c < 0,$$
where $text{Ei}$ is the exponential integral, $a,b, c, d$ are arbitrary real constants, and $gamma$ is the Euler-Mascheroni constant.
I have tried moving the terms around etc., to no avail; Mathematica also does not seem able to solve this.
I was wondering if there are any easy ways to solve this, or at least simplify it?
inequality optimization integral-inequality discrete-optimization functional-inequalities
asked Jan 1 at 16:45
jackson5jackson5
618513
$endgroup$
add a comment |
$begingroup$
I want to identify the least natural number $n$ (of course, it suffices to solve this problem for the reals, and then take the floor) such that
$$-c text{Ei}left(-e^{frac{a-d}{c}} (n+1)right)+a-b (n+1)+c log (n+1)+gamma c < 0,$$
where $text{Ei}$ is the exponential integral, $a,b, c, d$ are arbitrary real constants, and $gamma$ is the Euler-Mascheroni constant.
I have tried moving the terms around etc., to no avail; Mathematica also does not seem able to solve this.
I was wondering if there are any easy ways to solve this, or at least simplify it?
inequality optimization integral-inequality discrete-optimization functional-inequalities
asked Jan 1 at 16:45
jackson5jackson5
618513
$endgroup$
I want to identify the least natural number $n$ (of course, it suffices to solve this problem for the reals, and then take the floor) such that
$$-c text{Ei}left(-e^{frac{a-d}{c}} (n+1)right)+a-b (n+1)+c log (n+1)+gamma c < 0,$$
where $text{Ei}$ is the exponential integral, $a,b, c, d$ are arbitrary real constants, and $gamma$ is the Euler-Mascheroni constant.
I have tried moving the terms around etc., to no avail; Mathematica also does not seem able to solve this.
I was wondering if there are any easy ways to solve this, or at least simplify it?
inequality optimization integral-inequality discrete-optimization functional-inequalities
inequality optimization integral-inequality discrete-optimization functional-inequalities
asked Jan 1 at 16:45
jackson5jackson5
618513
asked Jan 1 at 16:45
jackson5jackson5
618513
asked Jan 1 at 16:45
jackson5jackson5
618513
asked Jan 1 at 16:45
jackson5jackson5
618513
asked Jan 1 at 16:45
jackson5jackson5
618513
618513
add a comment |
add a comment |
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