Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ai2t)

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=2, a₂>=2

For fixed z and a₁=2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=2, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ai2t.01

Input Form

HypergeometricPFQ[{2, 9/2}, {-(11/2), -(9/2)}, z] == (1/1031443875) (1031443875 + 375070500 z + 196465500 z^2 + 194594400 z^3 + 486486000 z^4 + 6616209600 z^5 - 293318625600 z^6 - 2909470233600 z^7 - 5667784254720 z^8 - 4376037657600 z^9 - 1689486197760 z^10 - 363562721280 z^11 - 45910364160 z^12 - 3447865344 z^13 - 150159360 z^14 - 3473408 z^15 - 32768 z^16) - (1/1031443875) (16384 E^z Sqrt[Pi] (54432000 z^(13/2) + 284860800 z^(15/2) + 446342400 z^(17/2) + 310262400 z^(19/2) + 113037120 z^(21/2) + 23496480 z^(23/2) + 2903040 z^(25/2) + 214920 z^(27/2) + 9270 z^(29/2) + 213 z^(31/2) + 2 z^(33/2)) 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]