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

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=4, a₂>=4

For fixed z and a₁=4, a₂=11/2, b₁>=-11/2

For fixed z and a₁=4, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{4, 11/2}, {-(7/2), -(7/2)}, -z] == (1/31255875) (31255875 - 56133000 z + 145945800 z^2 - 972972000 z^3 + 57891834000 z^4 - 2722764844800 z^5 + 12586271443200 z^6 - 19281501066240 z^7 + 13741344403200 z^8 - 5325214464000 z^9 + 1219945420800 z^10 - 172786360320 z^11 + 15408943104 z^12 - 859929600 z^13 + 28922880 z^14 - 532480 z^15 + 4096 z^16) - (1/31255875) ((512 Sqrt[Pi] (778377600 z^(9/2) - 11251094400 z^(11/2) + 36708940800 z^(13/2) - 47787667200 z^(15/2) + 31160959200 z^(17/2) - 11454397920 z^(19/2) + 2538254880 z^(21/2) - 351747360 z^(23/2) + 30908385 z^(25/2) - 1707285 z^(27/2) + 57006 z^(29/2) - 1044 z^(31/2) + 8 z^(33/2)) Erfi[Sqrt[z]])/E^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]