Some Formulas for the Products of E Functions And Whittaker Functions
Some Formulas for the Products of E Functions And Whittaker Functions
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In our eReader you can find the full English version of the book. Read Some Formulas for the Products of E Functions And Whittaker Functions 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 Some Formulas for the Products of E Functions And Whittaker Functions
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To quickly assess the difficulty of the text, read a short excerpt:
, . DXp. , o •'o , 00 __1 _2 / X ^ E(a, p::x)E (0, ^:: x^, . . TjX 2^ )dx.
Now, remeittberincT that thp differential equation 2 " » (6) z w - z(z+a+p-l)w ••• apw » has solutions F(a, p::z), z° ^F^(a}l-»-a-pjz) and z^ ^F^(p jl+p-ajz), we can write the last result, as . ?
-u - 2. I 1-i 3-1 b P f" (b) + 2(1- i)b PF'(bK(l. ^)(-i)b PF(b) . 00, 00 ' '" j ff' Jx;(^*l^/P E(a, p::x^)i dx^, ... , dXp_2 'O 'o X X P E(a, pt:x) |x^, . »«, x 2>* lx^, »»»>x 2»^ +a+p-l] where E - apE ). Dxj E = E(a, p:: —= j) ...X^»-»>Xp_2J Therefore ___ 2-i 1-i 2-i b^'PF''(b) ♦ 2(l-i)b Pp'Cb) Ml-i)(-i)b PF(b)-(a*p-l)b P 3-i l-i 1-i F (b) - (a+p-l)b PF(b) + apb P F(b) - L, where . 00, 00 L - b f D-2 I — J fr ^ x;^'*l^/P-2 E(a, p::xpl dx^, ... , dXp. 2 o / X P E(a, p::x)E (a, p:J rr ) dx.
O *^ To find L, we go back to the original definition of F(b), namely.
F(b) 00, 00 /o -'o p-1 T r-l Xj.^ K(a, B::x^) dx^, ... , dx, E(a, p:: ) so that - 5 - F (b) / E (a, p:: E(a, p::x^)V dx^, ... , dx _^ ).
X, » • • t ^'f-.
What to read after Some Formulas for the Products of E Functions And Whittaker Functions?
You can find similar books in the "Read Also" column, or choose other free books by F M Ragab to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, . DXp. , o •'o , 00 __1 _2 / X ^ E(a, p::x)E (0, ^:: x^, . . TjX 2^ )dx.
Now, remeittberincT that thp differential equation 2 " » (6) z w - z(z+a+p-l)w ••• apw » has solutions F(a, p::z), z° ^F^(a}l-»-a-pjz) and z^ ^F^(p jl+p-ajz), we can write the last result, as . ?
-u - 2. I 1-i 3-1 b P f" (b) + 2(1- i)b PF'(bK(l. ^)(-i)b PF(b) . 00, 00 ' '" j ff' Jx;(^*l^/P E(a, p::x^)i dx^, ... , dXp_2 'O 'o X X P E(a, pt:x) |x^, . »«, x 2>* lx^, »»»>x 2»^ +a+p-l] where E - apE ). Dxj E = E(a, p:: —= j) ...X^»-»>Xp_2J Therefore ___ 2-i 1-i 2-i b^'PF''(b) ♦ 2(l-i)b Pp'Cb) Ml-i)(-i)b PF(b)-(a*p-l)b P 3-i l-i 1-i F (b) - (a+p-l)b PF(b) + apb P F(b) - L, where . 00, 00 L - b f D-2 I — J fr ^ x;^'*l^/P-2 E(a, p::xpl dx^, ... , dXp. 2 o / X P E(a, p::x)E (a, p:J rr ) dx.
O *^ To find L, we go back to the original definition of F(b), namely.
F(b) 00, 00 /o -'o p-1 T r-l Xj.^ K(a, B::x^) dx^, ... , dx, E(a, p:: ) so that - 5 - F (b) / E (a, p:: E(a, p::x^)V dx^, ... , dx _^ ).
X, » • • t ^'f-.
What to read after Some Formulas for the Products of E Functions And Whittaker Functions?
You can find similar books in the "Read Also" column, or choose other free books by F M Ragab to read onlineMoreLess
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