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What hypergeometric transformation rules might I apply to try to simplify a certain expression?
$begingroup$
I have (https://mathematica.stackexchange.com/questions/189538/sum-a-certain-hypergeometric-function-based-expression-pertaining-to-an-integrat) a Mathematica expression involving the following six (regularized) hypergeometric functions: $, _3tilde{F}_2left(frac{3}{4},1,h-frac{1}{2};h+frac{3}{4},h+frac{5}{2};1right)$; $, _3tilde{F}_2left(frac{7}{4},2,h+frac{1}{2};h+frac{7}{4},h+frac{7}{2};1right)$;$, _3tilde{F}_2left(frac{11}{4},3,h+frac{3}{2};h+frac{11}{4},h+frac{9}{2};1right)$; $,
_4tilde{F}_3left(frac{3}{4},1,h+frac{1}{2},h+frac{1}{2};h+frac{3}{4};h+frac{3}{
2},h+frac{5}{2};1right)$;$,
_4tilde{F}_3left(frac{7}{4},2,h+frac{3}{2},h+frac{3}{2};h+frac{7}{4},h+frac{5}{
2},h+frac{7}{2};1right)$; and $,
_4tilde{F}_3left(frac{11}{4},3,h+frac{5}{2},h+frac{5}{2};h+frac{11}{4},h+frac{7
}{2},h+frac{9}{2};1right)$.
What (contiguous) transformation rules might I investigate applying in attempting to simplify the expression--noting that several of the arguments can be obtained from others by the addition/subtraction of 1?
Incidentally, on a strange note, I tried to access the NIST Handbook for
relevant information, but the website https://dlmf.nist.gov is inaccessible due to the current government shutdown.
special-functions transformation hypergeometric-function
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
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add a comment |
$begingroup$
I have (https://mathematica.stackexchange.com/questions/189538/sum-a-certain-hypergeometric-function-based-expression-pertaining-to-an-integrat) a Mathematica expression involving the following six (regularized) hypergeometric functions: $, _3tilde{F}_2left(frac{3}{4},1,h-frac{1}{2};h+frac{3}{4},h+frac{5}{2};1right)$; $, _3tilde{F}_2left(frac{7}{4},2,h+frac{1}{2};h+frac{7}{4},h+frac{7}{2};1right)$;$, _3tilde{F}_2left(frac{11}{4},3,h+frac{3}{2};h+frac{11}{4},h+frac{9}{2};1right)$; $,
_4tilde{F}_3left(frac{3}{4},1,h+frac{1}{2},h+frac{1}{2};h+frac{3}{4};h+frac{3}{
2},h+frac{5}{2};1right)$;$,
_4tilde{F}_3left(frac{7}{4},2,h+frac{3}{2},h+frac{3}{2};h+frac{7}{4},h+frac{5}{
2},h+frac{7}{2};1right)$; and $,
_4tilde{F}_3left(frac{11}{4},3,h+frac{5}{2},h+frac{5}{2};h+frac{11}{4},h+frac{7
}{2},h+frac{9}{2};1right)$.
What (contiguous) transformation rules might I investigate applying in attempting to simplify the expression--noting that several of the arguments can be obtained from others by the addition/subtraction of 1?
Incidentally, on a strange note, I tried to access the NIST Handbook for
relevant information, but the website https://dlmf.nist.gov is inaccessible due to the current government shutdown.
special-functions transformation hypergeometric-function
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
$endgroup$
add a comment |
$begingroup$
I have (https://mathematica.stackexchange.com/questions/189538/sum-a-certain-hypergeometric-function-based-expression-pertaining-to-an-integrat) a Mathematica expression involving the following six (regularized) hypergeometric functions: $, _3tilde{F}_2left(frac{3}{4},1,h-frac{1}{2};h+frac{3}{4},h+frac{5}{2};1right)$; $, _3tilde{F}_2left(frac{7}{4},2,h+frac{1}{2};h+frac{7}{4},h+frac{7}{2};1right)$;$, _3tilde{F}_2left(frac{11}{4},3,h+frac{3}{2};h+frac{11}{4},h+frac{9}{2};1right)$; $,
_4tilde{F}_3left(frac{3}{4},1,h+frac{1}{2},h+frac{1}{2};h+frac{3}{4};h+frac{3}{
2},h+frac{5}{2};1right)$;$,
_4tilde{F}_3left(frac{7}{4},2,h+frac{3}{2},h+frac{3}{2};h+frac{7}{4},h+frac{5}{
2},h+frac{7}{2};1right)$; and $,
_4tilde{F}_3left(frac{11}{4},3,h+frac{5}{2},h+frac{5}{2};h+frac{11}{4},h+frac{7
}{2},h+frac{9}{2};1right)$.
What (contiguous) transformation rules might I investigate applying in attempting to simplify the expression--noting that several of the arguments can be obtained from others by the addition/subtraction of 1?
Incidentally, on a strange note, I tried to access the NIST Handbook for
relevant information, but the website https://dlmf.nist.gov is inaccessible due to the current government shutdown.
special-functions transformation hypergeometric-function
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
$endgroup$
I have (https://mathematica.stackexchange.com/questions/189538/sum-a-certain-hypergeometric-function-based-expression-pertaining-to-an-integrat) a Mathematica expression involving the following six (regularized) hypergeometric functions: $, _3tilde{F}_2left(frac{3}{4},1,h-frac{1}{2};h+frac{3}{4},h+frac{5}{2};1right)$; $, _3tilde{F}_2left(frac{7}{4},2,h+frac{1}{2};h+frac{7}{4},h+frac{7}{2};1right)$;$, _3tilde{F}_2left(frac{11}{4},3,h+frac{3}{2};h+frac{11}{4},h+frac{9}{2};1right)$; $,
_4tilde{F}_3left(frac{3}{4},1,h+frac{1}{2},h+frac{1}{2};h+frac{3}{4};h+frac{3}{
2},h+frac{5}{2};1right)$;$,
_4tilde{F}_3left(frac{7}{4},2,h+frac{3}{2},h+frac{3}{2};h+frac{7}{4},h+frac{5}{
2},h+frac{7}{2};1right)$; and $,
_4tilde{F}_3left(frac{11}{4},3,h+frac{5}{2},h+frac{5}{2};h+frac{11}{4},h+frac{7
}{2},h+frac{9}{2};1right)$.
What (contiguous) transformation rules might I investigate applying in attempting to simplify the expression--noting that several of the arguments can be obtained from others by the addition/subtraction of 1?
Incidentally, on a strange note, I tried to access the NIST Handbook for
relevant information, but the website https://dlmf.nist.gov is inaccessible due to the current government shutdown.
special-functions transformation hypergeometric-function
special-functions transformation hypergeometric-function
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
asked Jan 16 at 1:50
Paul B. SlaterPaul B. Slater
22319
22319
add a comment |
add a comment |
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