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

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=-5/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(5/2), -(3/2)}, -z] == (1/637875) (637875 - 5613300 z + 170270100 z^2 + 13621608000 z^3 - 241491650400 z^4 + 789534345600 z^5 - 996601656960 z^6 + 625425909120 z^7 - 221241916800 z^8 + 47295622080 z^9 - 6343041600 z^10 + 541184136 z^11 - 29114592 z^12 + 949440 z^13 - 17024 z^14 + 128 z^15) - (1/637875) ((4 Sqrt[Pi] (13232419200 z^(7/2) - 112475563200 z^(9/2) + 280888171200 z^(11/2) - 309354066000 z^(13/2) + 179589992400 z^(15/2) - 60569729640 z^(17/2) + 12557228040 z^(19/2) - 1650046815 z^(21/2) + 138821850 z^(23/2) - 7395240 z^(25/2) + 239472 z^(27/2) - 4272 z^(29/2) + 32 z^(31/2)) 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]