Please solve the integral using some special function (preferably) [closed]
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when the integration involves two variables hypergeometric function is used to represent the below integral.$$ int_{0}^{infty} frac{1}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx}} dx hspace{1cm} a,b>0 $$
This integral can be turn out be Hypergeoometric function ${}_2F_1(alpha,beta;gamma;z)$.
newline
But the integral contains four variables of similar type of expression how to reduce the function I don't know. I want to know the result of this integral. Iam very happy if anyone giving hint atleast.
$$ int_{0}^{infty} frac{e^{-(a+b)x }}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx} + c hspace{0.03cm} e^{-cx} + d hspace{0.03cm} e^{-dx}} dx hspace{1cm} a,b,c,d >0 $$
special-functions closed-form
asked Dec 3 at 4:45
hanu
13
closed as off-topic by Martin R, Nosrati, abiessu, mathematics2x2life, achille hui Dec 3 at 5:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Martin R, Nosrati, abiessu, mathematics2x2life, achille hui
If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
-4
down vote
favorite
when the integration involves two variables hypergeometric function is used to represent the below integral.$$ int_{0}^{infty} frac{1}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx}} dx hspace{1cm} a,b>0 $$
This integral can be turn out be Hypergeoometric function ${}_2F_1(alpha,beta;gamma;z)$.
newline
But the integral contains four variables of similar type of expression how to reduce the function I don't know. I want to know the result of this integral. Iam very happy if anyone giving hint atleast.
$$ int_{0}^{infty} frac{e^{-(a+b)x }}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx} + c hspace{0.03cm} e^{-cx} + d hspace{0.03cm} e^{-dx}} dx hspace{1cm} a,b,c,d >0 $$
special-functions closed-form
asked Dec 3 at 4:45
hanu
13
closed as off-topic by Martin R, Nosrati, abiessu, mathematics2x2life, achille hui Dec 3 at 5:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Martin R, Nosrati, abiessu, mathematics2x2life, achille hui
If this question can be reworded to fit the rules in the help center, please edit the question.
7
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Kemono Chen
Dec 3 at 4:49
add a comment |
up vote
-4
down vote
favorite
up vote
-4
down vote
favorite
when the integration involves two variables hypergeometric function is used to represent the below integral.$$ int_{0}^{infty} frac{1}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx}} dx hspace{1cm} a,b>0 $$
This integral can be turn out be Hypergeoometric function ${}_2F_1(alpha,beta;gamma;z)$.
newline
But the integral contains four variables of similar type of expression how to reduce the function I don't know. I want to know the result of this integral. Iam very happy if anyone giving hint atleast.
$$ int_{0}^{infty} frac{e^{-(a+b)x }}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx} + c hspace{0.03cm} e^{-cx} + d hspace{0.03cm} e^{-dx}} dx hspace{1cm} a,b,c,d >0 $$
special-functions closed-form
asked Dec 3 at 4:45
hanu
13
when the integration involves two variables hypergeometric function is used to represent the below integral.$$ int_{0}^{infty} frac{1}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx}} dx hspace{1cm} a,b>0 $$
This integral can be turn out be Hypergeoometric function ${}_2F_1(alpha,beta;gamma;z)$.
newline
But the integral contains four variables of similar type of expression how to reduce the function I don't know. I want to know the result of this integral. Iam very happy if anyone giving hint atleast.
$$ int_{0}^{infty} frac{e^{-(a+b)x }}{a hspace{0.03cm} e^{-ax} + bhspace{0.03cm} e^{-bx} + c hspace{0.03cm} e^{-cx} + d hspace{0.03cm} e^{-dx}} dx hspace{1cm} a,b,c,d >0 $$
special-functions closed-form
special-functions closed-form
asked Dec 3 at 4:45
hanu
13
asked Dec 3 at 4:45
hanu
13
edited Dec 4 at 15:27
asked Dec 3 at 4:45
hanu
13
asked Dec 3 at 4:45
hanu
13
asked Dec 3 at 4:45
hanu
13
13
closed as off-topic by Martin R, Nosrati, abiessu, mathematics2x2life, achille hui Dec 3 at 5:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Martin R, Nosrati, abiessu, mathematics2x2life, achille hui
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Martin R, Nosrati, abiessu, mathematics2x2life, achille hui Dec 3 at 5:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Martin R, Nosrati, abiessu, mathematics2x2life, achille hui
If this question can be reworded to fit the rules in the help center, please edit the question.
7
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Kemono Chen
Dec 3 at 4:49
add a comment |
7
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Kemono Chen
Dec 3 at 4:49
7
7
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Kemono Chen
Dec 3 at 4:49
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Kemono Chen
Dec 3 at 4:49
add a comment |
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7
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Kemono Chen
Dec 3 at 4:49