polyanin integral equations errata
PDF · 2 pages · 45.0 KB
Open PDF file
Two-page errata sheet distributed by EqWorld for the Handbook of Integral Equations by A. D. Polyanin and A. V. Manzhirov. It gives was/correct pairs for specific pages, including pages 42, 217, 428, 465, 477, 733 and 761-763. The corrections cover equations, table entries, the Euler constant value, the incomplete beta function and conditions on parameters. It is a reference item kept with Phil's integral equations files.
AI-written summary; may contain errors.
Extracted text (machine-read; may contain errors)
EqWorld http://eqworld.ipmnet.ru
Listof Errata
Handbook of Integral Equations, CRC Press, 1998 by A. D. Polyanin and
A.V.Manzhirov
Page 42: Equation2:
Was:...f(a)=f0
x(a)=fxx(x)= 0.
Correct: ...f(a)=f0
x(a)=fxx(a)= 0.
Page217: Equation2, the solution in Item 2±:
Was:
y(x)=1
¼2p(x−a)(b−x)h
: : :+1
¼ln£1
4(b−a)¤: : :i
Correct:
y(x)=1
¼2p(x−a)(b−x)h
: : :+1
ln£1
4(b−a)¤: : :i
Page428: Line2:
Was:... iff(x)is measurable and
Correct: ... iff(x,t)ismeasurable and
Page465: Fig. 2, formula in the third box from top:
Was:ey(p)=ef(p)
1−eK(p)≡ef(p)−eK(p)
1−eK(p)ef(p)
Correct: ey(p)=ef(p)
1−eK(p)≡ef(p)+eK(p)
1−eK(p)ef(p)
Page477: Table5, row5, column 2:
Was: Axnx¸
Correct: Ax¸lnnx
Page733: Section6.2, row4 in the table, column 3:
Was:¼
2ae−au(theintegralis understood
inthe sense of Cauchyprincipal value)
Correct:¼
2ae−au
Page733: Section6.2, row5 in the table, column 3:
Was:¼sin(au)
2u
Correct:¼sin(au)
2u(the integralis understood
inthe sense of Cauchyprincipal value)
Page761: Lastline:
Was: : : :(|arg|z<¼).
Correct: : : :(|argz|<¼).
Page762: Formulaon the third line from top:
Was:
Ã(z)=ln¡(z)
dz=¡0
z(z)
¡(z).
Correct:
Ã(z)=dln¡(z)
dz=¡0
z(z)
¡(z).
Page762: line14:
Was:where C= −Ã(1)=0.5572: : :is the Euler constant.
Correct: where C= −Ã(1)=0.5772: : :is the Euler constant.
Remark. A similar misprint also appears at some other places of the book.
Page763: Section10.5, Last displayed formula:
Was:
Bx(p,q)=Z1
0tp−1(1−t)q−1dt,
Correct:
Bx(p,q)=Zx
0tp−1(1−t)q−1dt,
Page763: Lineright before Section 10.6:
Was:whereRe x>0andRe y>0.
Correct: whereRe p>0and Re q>0.