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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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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