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- W2162371170 abstract "It is shown how sums of squares of real valued functions can be used to give new proofs of the reality of the zeros of the Bessel functions Jα(z) when α ≥ – 1, confluent hypergeometric functions F 0 1 ( c ; z ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072133/119ac5a2-c416-4d47-b96f-0f732d823fac/content/eq2407.tif/> when c>0 or 0>c>–1, Laguerre polynomials L n α ( z ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072133/119ac5a2-c416-4d47-b96f-0f732d823fac/content/eq2408.tif/> when α ≥ – 2, and Jacobi polynomials P n ( α , β ) ( z ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072133/119ac5a2-c416-4d47-b96f-0f732d823fac/content/eq2409.tif/> when α ≥ – 1 and β > – 1. Besides yielding new inequalities for | F ( z ) | 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072133/119ac5a2-c416-4d47-b96f-0f732d823fac/content/eq2410.tif/> where F(z) is one of these functions, the derived identities lead to inequalities for ∂ | F ( z ) | 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072133/119ac5a2-c416-4d47-b96f-0f732d823fac/content/eq2411.tif/> and ∂ | F ( z ) | 2 / ∂ y https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072133/119ac5a2-c416-4d47-b96f-0f732d823fac/content/eq2412.tif/> and ∂ 2 | F ( z ) | 2 / ∂ y 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072133/119ac5a2-c416-4d47-b96f-0f732d823fac/content/eq2413.tif/> which also give new proofs of the reality of the zeros." @default.
- W2162371170 created "2016-06-24" @default.
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- W2162371170 date "2020-12-17" @default.
- W2162371170 modified "2023-09-26" @default.
- W2162371170 title "Using Sums of Squares to Prove That Certain Entire Functions Have Only Real Zeros" @default.
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