Integral Identities Involving Zonal Polynomials
Integral Identities Involving Zonal Polynomials
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In our eReader you can find the full English version of the book. Read Integral Identities Involving Zonal Polynomials Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Integral Identities Involving Zonal Polynomials
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1) Proof : Define for Re A = and a, P > 7 - 1, -tr A U I, cc-y l3(A, a, P) = B;^a, P) / I, J ''= u>o li"^!
Th en as j^FQ(a+p5 -U) = | I+U | " ^"^"^ ^, 'For another way of deriving first and second moments of iB(I, cc, P) see Martin [7].
- 19 Ib(a, a, P) = B;\a, P) J e-'^ 4 y |y|a-7 iFo(a+P; -y) dy u > q and this equals (5. 1) by virtue of definition H(2, l).
Expression (5. 1) for the characteristic function of y is not in a form con- venient for computing moments of U. Theorem 1, however, gives... us an easy way of finding them. Since the characteristic function , -tr AU, «1^ ~k" 1, ^^^ = =) = k?0 kl ^^'^"^ 4 y) = k?0 ^ kT ^^^K^'^ y^^ ' K matching coefficients of appropriate powers of elements of A in the two expan- sions will give the moments.
Write (5. 1) as an iterated Laplace transform 1 U > (5. 2) rm(«)VP) J o^o(-4 y) e-^^ ^ i |yr^ / -tr Z, ia+3-7 J / e = |zj dU dZ z > q Then by definition H(2ol), (5. 2) is " z > q A generic term in the expansion of (5. 3) in zonal polynomials is -^^^ ^ C (-AZ_-b e-'^'^^= |z|^''dZ_ k: ?„, (?) J K Z > and by Theorem 1, provided p > k - y - l, this term is 20 5^(P.
What to read after Integral Identities Involving Zonal Polynomials?
You can find similar books in the "Read Also" column, or choose other free books by G M Kaufman to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
1) Proof : Define for Re A = and a, P > 7 - 1, -tr A U I, cc-y l3(A, a, P) = B;^a, P) / I, J ''= u>o li"^!
Th en as j^FQ(a+p5 -U) = | I+U | " ^"^"^ ^, 'For another way of deriving first and second moments of iB(I, cc, P) see Martin [7].
- 19 Ib(a, a, P) = B;\a, P) J e-'^ 4 y |y|a-7 iFo(a+P; -y) dy u > q and this equals (5. 1) by virtue of definition H(2, l).
Expression (5. 1) for the characteristic function of y is not in a form con- venient for computing moments of U. Theorem 1, however, gives... us an easy way of finding them. Since the characteristic function , -tr AU, «1^ ~k" 1, ^^^ = =) = k?0 kl ^^'^"^ 4 y) = k?0 ^ kT ^^^K^'^ y^^ ' K matching coefficients of appropriate powers of elements of A in the two expan- sions will give the moments.
Write (5. 1) as an iterated Laplace transform 1 U > (5. 2) rm(«)VP) J o^o(-4 y) e-^^ ^ i |yr^ / -tr Z, ia+3-7 J / e = |zj dU dZ z > q Then by definition H(2ol), (5. 2) is " z > q A generic term in the expansion of (5. 3) in zonal polynomials is -^^^ ^ C (-AZ_-b e-'^'^^= |z|^''dZ_ k: ?„, (?) J K Z > and by Theorem 1, provided p > k - y - l, this term is 20 5^(P.
What to read after Integral Identities Involving Zonal Polynomials?
You can find similar books in the "Read Also" column, or choose other free books by G M Kaufman to read onlineMoreLess
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