Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anv7)

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=-1/2

http://functions.wolfram.com/07.25.03.anv7.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(1/2), 5/2}, -z] == (1/37800) (37800 + 997920 z - 7567560 z^2 + 11861850 z^3 - 7248150 z^4 + 2122605 z^5 - 323876 z^6 + 26088 z^7 - 1040 z^8 + 16 z^9) - (1/75600) ((Sqrt[Pi] z^(3/2) (5405400 - 22972950 z + 29459430 z^2 - 16351335 z^3 + 4545450 z^4 - 672840 z^5 + 53200 z^6 - 2096 z^7 + 32 z^8) 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]