Two exponential integrals

[Augustrush]

   
   

The ∆h, F, x1, x2,δ are constant, how to generate these two exponential integrals? I have tried to use the theorem of residue, but this seems not work while there is no singularity points but only zeros points in the integrand functions. So is there any other ways to solve these?
Thank you very much!

[tommy1729]

The ∆h, F, x1, x2,δ are constant, how to generate these two exponential integrals? I have tried to use the theorem of residue, but this seems not work while there is no singularity points but only zeros points in the integrand functions. So is there any other ways to solve these?
Thank you very much!

for starters i think your two functions are distinct , not ?

you start to write for both f(a) = ... yet i think they differ , already by the amount of parameters.

secondly , an integral with 2 or more parameters is usually not solvable in simple functions , see e.g. the integral definition of the gamma function.

maybe meijer G like functions ...


third : why do you consider these functions important ? for calculus or for tetration ?

welcome to the forum.

regards

tommy1729

[Augustrush]

The ∆h, F, x1, x2,δ are constant, how to generate these two exponential integrals? I have tried to use the theorem of residue, but this seems not work while there is no singularity points but only zeros points in the integrand functions. So is there any other ways to solve these?
Thank you very much!

for starters i think your two functions are distinct , not ?

you start to write for both f(a) = ... yet i think they differ , already by the amount of parameters.

secondly , an integral with 2 or more parameters is usually not solvable in simple functions , see e.g. the integral definition of the gamma function.

maybe meijer G like functions ...


third : why do you consider these functions important ? for calculus or for tetration ?

welcome to the forum.

regards

tommy1729

Thank you for your help.
Firstly, yes. These are two different infinite integrals, and the results would be two functions of the variable A. And I am quite interested in these functions as these two exponential integrals are closely related to a model validation of my current research work, but it seems a little hard for me to get through...

AugustRush