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

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=1, a₂>=1

For fixed z and a₁=1, a₂=11/2, b₁>=-11/2

For fixed z and a₁=1, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1, 11/2}, {-(11/2), -(11/2)}, z] == (1/102112943625) (102112943625 + 18565989750 z + 5959453500 z^2 + 3648645000 z^3 + 4962157200 z^4 + 20951330400 z^5 + 879955876800 z^6 + 30014020713600 z^7 + 102798200736000 z^8 + 118451012359680 z^9 + 63863198530560 z^10 + 18686050437120 z^11 + 3200570265600 z^12 + 332430336000 z^13 + 21025767424 z^14 + 785154048 z^15 + 15794176 z^16 + 131072 z^17) + (1/102112943625) (131072 E^z Sqrt[Pi] (39916800 z^(13/2) + 439084800 z^(15/2) + 1097712000 z^(17/2) + 1097712000 z^(19/2) + 548856000 z^(21/2) + 153679680 z^(23/2) + 25613280 z^(25/2) + 2613600 z^(27/2) + 163350 z^(29/2) + 6050 z^(31/2) + 121 z^(33/2) + z^(35/2)) 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]