Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anrg)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.anrg.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), -(7/2)}, z] == (1/15471658125) (15471658125 + 26522842500 z + 53635081500 z^2 + 204324120000 z^3 + 3126159036000 z^4 - 79196028912000 z^5 + 2032698075408000 z^6 + 20101982805273600 z^7 + 48311124811488000 z^8 + 51185156645145600 z^9 + 29425899355776000 z^10 + 10210727697408000 z^11 + 2275975296000000 z^12 + 338361649920000 z^13 + 34262237399040 z^14 + 2381034044160 z^15 + 112904467200 z^16 + 3571304448 z^17 + 71720960 z^18 + 823296 z^19 + 4096 z^20) + (1/15471658125) (128 E^z Sqrt[Pi] (46705350384000 z^(13/2) + 264663652176000 z^(15/2) + 515590436592000 z^(17/2) + 489080691792000 z^(19/2) + 263269882260000 z^(21/2) + 87605016760800 z^(23/2) + 18988667497800 z^(25/2) + 2768971451400 z^(27/2) + 276566033205 z^(29/2) + 19029582495 z^(31/2) + 895744290 z^(33/2) + 28177800 z^(35/2) + 563520 z^(37/2) + 6448 z^(39/2) + 32 z^(41/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]