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. 2 - .

. , . . 2 .: , 1973. 297 c.
( ): visshietransfunkciit21974.djvu
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=0

* 2

+ cos (-? (-lrfn+i^m + l)^)-2"1-1

=



_2_

-1

je

sin (-2 (-1)( + -.2/+)(2*)-

m=u

. (1)

3m 1

. (2)

- cos (- -f-) 2 (-1)"1 ("+ J. 2/n) (2)~

m=0



1' 1 () = /-"-V V + /n) (2z)~m, (3)



WpS () - /ntl^i2 2 (-Om (+J. /) (2*), (4)

Iti^d 90 . 7. . (7.18.1

J , () = (-1)+1^ ,(); ,<*)(-!) ,(), ' (5)

-- + --- +- * '

'*

,/X





MV)--1\<)--tV^

2 ~ * *

Hf(z)-IH<\ W-/-|/X,-i

(6)

(7)

(8) )

(10)

"' ,() = /(-1)"11' , (z); '2' , () = -/(-1)"'2 . (), -- + +2

.-/'-^,

2

, ,-_,/^^)'^!.

- /I"'--o-^'ai. ,

> (*> - 1 (Z) j/^j- sin . (14)

2

! ()--J (z)--cos , (I5)

H ~2

I1 (*)-~lA^rt , (16)

(12) (13)

(17)

(18)

- .

(-) l*V 'v ()|" 7V-" <*> (19>

wu_v '*{z)]" *~v~w /v+()- (20) .1] 7.1t. 91

-f l*V **()1 = (_1) iz)- (21)

" l*~v ()]" (~1> *~~ + {) (22)

/v_, () /v+) () = 2v*-' Zv (). (23)

Zv-. W +/v+1 W =-2/;(), (24)

ChW-^IW--2vz-'/Cv(z), (25)

Kv_, ()+ tfv+i W ---2<(). (26)

.

W(! W2) = J2 W1W2,

W(Jy,J v) = -^|-sin(vn), ' (27)

(28) (29)

r(t".iff). ()

(31)

IP(ZviKv)--*-1. (32)

yv (z) -v+i ()+/_v () /v_, () - 2s'"(VJt), (33)

^v" () ()^^, (#) // (*) ^ _ -, (34)

/v W lVi (*>* W -Zv-I W - (35)

Vi W (^) -Zv(), () = A-, (36)

^v M "1- W -Vi () (*> - , (37)

ZvW /_v+1 () -/_v () V1 ()--ISSjA, (38)

JlZ

Kv+1 () /v (*) + Kv (*) Vi (*) - (39)

<.( ).

yv (*') = e'm3tv Zv (), (40)

Yv (zetmn) = #-'* Kv +2/ ^ff cos (rtv) /v (*), (41)

Si (), (42, 93 . 7. . (7.18.1

f (**"*) - slntITn^nvl Mf (z) -?^ Hf (Z), (43)

lv(zeimn) = elmm lv(z), (44)

Ky (Uteut) - *"'mJ,v Kv (z) - in /v (*) (45) V , ,

v-> Sln (nv) v ' I 1, +1.

7.12.

.



Jn (z) = J cos (z sin < /) d(f, (1)





Jn (Z) = " J " 008 cos () <, (2)





2

! (z) "2 J cos ( sin ) cos (2) /, (3)

2

/+1 ^"2J sin sln ) sln 1(2 + Բ rfV- (4)

(1)-(4) /, 1, 2,... .



T

(v + 2)7v w " J7 (2)V Icoa (*,ln ) (co *)8v ** (5)

fc 0 *

Jt

'2

I J*tn41\ *



(6)

IJJl 7.18. 94

= TtHfj U-V1



(5)-(10) Rev> -j. . Ivn I

nYv(z)= 2 I /JVi*008'cos(Vf)A

qd

J '2 ch' [ (V/ /vai) + ~ch (W)] dt



.

2

(8) (9) ()

0 < arg * < . (11)

-4

>0, < Re v< .



Jv (Jt) - 2 J sin (je Chf--^y-) Ch (Vf) dt,



Itrv(Jf)--2 J* eoi(*ch*-y-)ch(*) dt.

sin (xt) dt, (12)

cos (xt) dt. (13)

(14) (W)

(14) (15) *>0, 1 < Rev< 1.



J

JiJ4(X)= j* -v'sln^ch< j* cos(xsint vtf)dt.

(18)

>0, Rev>0. 94 . . . .

(Lambe. 1931):

V _

JyiV&^y*) J cos (Jt sln t -V*) dt -





8() J e-vte-ytht-xabtdt, Re (Jt +) >0, (17)

V _ *

j?2.j2 Yv(yx2_yt)^ J Sco"Sln(XSlttt-Vt)dt-



_ J (ev<+ych t + e-v/-ych< cos ' Ihtdt Re : > Re > 0. (18)



.

OO j

(-j-v)Kv(*)-rs(7)V j" -"V1-I)'v'Jdt,

(19)

Re - 0, Revc-I,

OO

(I + v) KvW=/H(i-)V J" ,-'ch'(8h O2v dt,

(20)

Re >0, Rev>

Kv () - J ~** * ch (vf) dt, Re > 0, (21)



OO J 1

(v +1) Ky (z) - /f -' J (l + 4)V~ dt, (22)

Re* > O1 Rev> ,

00

Kv(M)-Ip j* Re * > O1 Re (a2z) > 0. (23)

t\n 03

? J exp [(t -^)-*]*-1 dt, (24)

IJJl 7.18. 96



Kv (JC) COS (-^r) = J cos (JC sh t) ch (vt) dt, (25)





Ky (Je) sin I^j = J sin (x Sh sh (vt) dt. (26)

O

(25) (26) je > 0, l < Re v < l.

l

K4(Z) - - (v +1) J ('* -Ms) V 2 cos t dt, Rev>i. |arg*|'<|-.

.

Im z > 0, Re v < ^,

Im > 0, Re V < -g-.

UVTTii



Im < 0, Rev<-i-,

(27)

(28)

(29)

Im < 0, Rev < ,

-(^-̯'-'-"-

(31)

- , te-- 1

(v+ ) '1' (*) - f (l 4- ?) 2 at. (32)



Rev>~i. |SI<i, 4_<18<+^,

(,+ >) f W- /Z' (, _ ,,

u

Rev>-i, |O|<J, + 06 . 7. . 17.19

*.

- +<

' <v* 1 2s

2//>(*)--2 J (-V-*) (-*)(--?) rfs. (34)

їI oo

I arg (--/2)1 C-J, 2<* ()- 2 J (V s)T(s) 'ds, (35)

-C-Ioo

I arg (te)I < -2.; ї , , Rev.
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