Product of evenly spaced factorials
I am attempting to get a closed form expression for a product of factorials $$(a!)cdot(2a)!cdots (na)!$$ where $a$ is a positive integer. Mathematica seems able to compute this whichever $a$ I give it. For example for $a = 15$ the expression equals
and for higher $a$ this expression gets uglier. However Mathematica strikes out for the general expression. I am asking for a general formula to compute this.
factorial products
asked Nov 28 '18 at 11:00
SweSnow
1233
add a comment |
I am attempting to get a closed form expression for a product of factorials $$(a!)cdot(2a)!cdots (na)!$$ where $a$ is a positive integer. Mathematica seems able to compute this whichever $a$ I give it. For example for $a = 15$ the expression equals
and for higher $a$ this expression gets uglier. However Mathematica strikes out for the general expression. I am asking for a general formula to compute this.
factorial products
asked Nov 28 '18 at 11:00
SweSnow
1233
you can't get a "closed form" because there is not a closed form for a simple factorial $n!$. You can write it also as $prod_{j=1}^{na}exp((n+1-lceil j/arceil)log j)$
– Masacroso
Nov 28 '18 at 14:11
add a comment |
I am attempting to get a closed form expression for a product of factorials $$(a!)cdot(2a)!cdots (na)!$$ where $a$ is a positive integer. Mathematica seems able to compute this whichever $a$ I give it. For example for $a = 15$ the expression equals
and for higher $a$ this expression gets uglier. However Mathematica strikes out for the general expression. I am asking for a general formula to compute this.
factorial products
asked Nov 28 '18 at 11:00
SweSnow
1233
I am attempting to get a closed form expression for a product of factorials $$(a!)cdot(2a)!cdots (na)!$$ where $a$ is a positive integer. Mathematica seems able to compute this whichever $a$ I give it. For example for $a = 15$ the expression equals
and for higher $a$ this expression gets uglier. However Mathematica strikes out for the general expression. I am asking for a general formula to compute this.
factorial products
factorial products
asked Nov 28 '18 at 11:00
SweSnow
1233
asked Nov 28 '18 at 11:00
SweSnow
1233
asked Nov 28 '18 at 11:00
SweSnow
1233
asked Nov 28 '18 at 11:00
SweSnow
1233
asked Nov 28 '18 at 11:00
SweSnow
1233
1233
you can't get a "closed form" because there is not a closed form for a simple factorial $n!$. You can write it also as $prod_{j=1}^{na}exp((n+1-lceil j/arceil)log j)$
– Masacroso
Nov 28 '18 at 14:11
add a comment |
you can't get a "closed form" because there is not a closed form for a simple factorial $n!$. You can write it also as $prod_{j=1}^{na}exp((n+1-lceil j/arceil)log j)$
– Masacroso
Nov 28 '18 at 14:11
you can't get a "closed form" because there is not a closed form for a simple factorial $n!$. You can write it also as $prod_{j=1}^{na}exp((n+1-lceil j/arceil)log j)$
– Masacroso
Nov 28 '18 at 14:11
you can't get a "closed form" because there is not a closed form for a simple factorial $n!$. You can write it also as $prod_{j=1}^{na}exp((n+1-lceil j/arceil)log j)$
– Masacroso
Nov 28 '18 at 14:11
add a comment |
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you can't get a "closed form" because there is not a closed form for a simple factorial $n!$. You can write it also as $prod_{j=1}^{na}exp((n+1-lceil j/arceil)log j)$
– Masacroso
Nov 28 '18 at 14:11