Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ank0)

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=5, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-3/2

http://functions.wolfram.com/07.25.03.ank0.01

Input Form

HypergeometricPFQ[{5, 6}, {-(3/2), 2}, -z] == (1/276480) (276480 + 2764800 z + 38707200 z^2 - 187348455 z^3 + 221057370 z^4 - 109335924 z^5 + 27036120 z^6 - 3581520 z^7 + 255456 z^8 - 9152 z^9 + 128 z^10) + (1/552960) ((Sqrt[Pi] (-173918745 z^(5/2) + 530038080 z^(7/2) - 531376560 z^(9/2) + 242686080 z^(11/2) - 57420000 z^(13/2) + 7409664 z^(15/2) - 519936 z^(17/2) + 18432 z^(19/2) - 256 z^(21/2)) 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]