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How to transform a definite a nested product into nested indefinite products?
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A nested product is said to be indefinite if its multiplicand is free of all of its upper bound variables. Otherwise, it is said to be a definite product. For example, $$prod_i=1^nprod_j=1^iprod_k=1^jfrack^22,k+1$$ is a nested indefinite product since its multiplicand, $frack^22,k+1$ is free of all the upper bound variables $n, i, j$. However, $$prod_i=1^nprod_j=1^iprod_k=1^jfraci+j+ki+j+k+2$$ is a definite product since its multiplicand $fraci+j+ki+j+k+2$ has the upper bound variables $i$ and $j$. Is there a general method of transforming a (nested) definite product to an indefinite (nested) product or a product of indefinite (nested) products?
generating-functions products
asked Jul 23 at 11:07
saintdoe
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A nested product is said to be indefinite if its multiplicand is free of all of its upper bound variables. Otherwise, it is said to be a definite product. For example, $$prod_i=1^nprod_j=1^iprod_k=1^jfrack^22,k+1$$ is a nested indefinite product since its multiplicand, $frack^22,k+1$ is free of all the upper bound variables $n, i, j$. However, $$prod_i=1^nprod_j=1^iprod_k=1^jfraci+j+ki+j+k+2$$ is a definite product since its multiplicand $fraci+j+ki+j+k+2$ has the upper bound variables $i$ and $j$. Is there a general method of transforming a (nested) definite product to an indefinite (nested) product or a product of indefinite (nested) products?
generating-functions products
asked Jul 23 at 11:07
saintdoe
112
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
A nested product is said to be indefinite if its multiplicand is free of all of its upper bound variables. Otherwise, it is said to be a definite product. For example, $$prod_i=1^nprod_j=1^iprod_k=1^jfrack^22,k+1$$ is a nested indefinite product since its multiplicand, $frack^22,k+1$ is free of all the upper bound variables $n, i, j$. However, $$prod_i=1^nprod_j=1^iprod_k=1^jfraci+j+ki+j+k+2$$ is a definite product since its multiplicand $fraci+j+ki+j+k+2$ has the upper bound variables $i$ and $j$. Is there a general method of transforming a (nested) definite product to an indefinite (nested) product or a product of indefinite (nested) products?
generating-functions products
asked Jul 23 at 11:07
saintdoe
112
A nested product is said to be indefinite if its multiplicand is free of all of its upper bound variables. Otherwise, it is said to be a definite product. For example, $$prod_i=1^nprod_j=1^iprod_k=1^jfrack^22,k+1$$ is a nested indefinite product since its multiplicand, $frack^22,k+1$ is free of all the upper bound variables $n, i, j$. However, $$prod_i=1^nprod_j=1^iprod_k=1^jfraci+j+ki+j+k+2$$ is a definite product since its multiplicand $fraci+j+ki+j+k+2$ has the upper bound variables $i$ and $j$. Is there a general method of transforming a (nested) definite product to an indefinite (nested) product or a product of indefinite (nested) products?
generating-functions products
asked Jul 23 at 11:07
saintdoe
112
edited Jul 24 at 7:26
asked Jul 23 at 11:07
saintdoe
112
asked Jul 23 at 11:07
saintdoe
112
asked Jul 23 at 11:07
saintdoe
112
112
add a comment |Â
add a comment |Â
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