xte-r dz, (6) * da, (e) dz. 9.29. Evaluate (a)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help number 9.29. Doing step by step. Thanks
Transcribed Image Text:Supplementary Problems
GAMMA FUNCTION
F(7)
(a)
2 r(4) r(3)
r(3) T(3/2)
(6)
T(9/2)
9.28.
Evaluate
(с) г(1/2) г(8/2) г (5/2).
te- dx,
e- dz,
9.29.
Evaluate
(a)
(b)
(e)
S* dz, (b)
9.80.
Find
(a)
(c)
9.31.
Show that
> 0.
9.32.
Prove that
l(n) =
da, n> 0,
L' (a In zj* dz,
S' Vin (1/2) dz.
9.33.
Evaluate
(a)
(In x)* dz, (b)
(0)
9.34.
Evaluate
(a) г(-7/2), (ь) г(-1/3).
9.35.
Prove that
lim r(*) = * where m = 0,1,2, 3, ...
Prove that if m is a ponitive integer, r(-m + 1) =
(-1)m 2" V
1-3-5... (2m – 1)
9.36.
222
GAMMA, BETA AND OTHER SPECIAL FUNCTIONS
9.37.
Prove that r'(1) =
e-- In z de is a negative number (it is equal to -y, where y
is called Euler's constant).
Obtain the miscellaneous result 4 on page 211 from the result (4) of Problem 9.23,
[Hint: Expand e/(sVn) + ... in a power series and replace the lower limit of the
-«.)
9.38.
BETA FUNCTION
9.39.
Evaluate (a) в(3, 5), (6) в(3/2, 2),
(c) B(1/3, 2/3).
9.40.
Find
(а)
x(1- 2)" da, (6)
(4- *)3/2 da.
9.41.
Evaluate (a)
{r(1/4)}
dy
J. Tai-y
9,42.
Prove that
%3D
9.43.
Evaluate
(a)
Bin e con e de,
(b)
cor e de.
9.44.
Evaluate (a)
sins e de,
(b)
cos e sin? e de.
9.45.
Prove that
Vtan e de = z/y2.
z dz
y dy
S, , N
9.46.
Prove that
(a)
(b)
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