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 New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | MEDIUM | LARGE Below is the OCR-scanned text from this page: 506 CONFLUENT HYPERGEOMETRIC FUNCTIONS 13.2.8 r(a)U(a, b, Z ) Similar integrals for Mc,,,(z) and Wc,,,(z) can be deduced with the help of.,13.1.32' and 13.1.33. Barnes-type Contour Integrals 13.2.9 for larg (-z)lO) 13.3.5 - *-1(2rn (YZ,, * n-0 (-I),, Ib-a-f+n(\$') (b#0,-1J-2J * . a) 13.3.7 - 5 A,, (iz)+"( b -24 -)"Jb-,+,, (J(2zb -&a)) n=O where &=I, Ai=O, Az=\$b, (la + 1 )&+I= (n + b- 1 ) A n -I + ( 2 ~ - a) A,, -2, (a real) 13.3.8 M(a,b,z) r(b) m n -0 =eh' C~Z"(-aZ)'"-b-n'~~-l+,,(2J(-UZ)) where co= 1, c, = - bh, c, = -+(2h-- 1)a +#b(b + l)h2, (n+ 1 ) c,,,, = [ (1 - 2h)n - bh]C,, +[(1-2h)u-h(h-l)(b+n-- 1)]C,,-1 -h(h- l)aC,,-2 (h real) 13.3.9 M(a, b, z)=2CR(a, b)l,,(z) where co = 1, c, (a, b) = 2a/b, n=O CJI+l(a, b)=2aC,,(a+l, b+l)/b-cC,-l(aJ 13.4. Recurrence Relations and Differential Properties 13.4.1 (b-a)M(a-l, b, z)+(2a-6+z)M(a, 6, 2) -aM(a+l, b, z)=O 13.4.2 b(b-l)M(a, b-1, z)+b(l-b-z)M(a, b, 2) +z(b--a)M(a, b+lJ z)=O 13.4.3 (l+a-b)M(a, b, z)-aM(a+l, b, 2) +(b-l)M(a, b-1, z)=O 13.4.4 bM(a, b, z)-bM(a-l, b, z)-zM(a, b+l, z)=O 13.4.5 b(a+z)M(a, 6, z)+z(a-b)Wa, b+1, z> -ubM(a+l, b, z)=O The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States.