Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.8089)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=5, b₁=7/2

http://functions.wolfram.com/07.25.03.8089.01

Input Form

HypergeometricPFQ[{-(7/2), 5}, {7/2, 6}, z] == 40/(2431 z^5) + (1/(14936064 z^5)) (E^z (-245760 + 245760 z - 122880 z^2 - 724805 z^3 - 1687630 z^4 + 7684008 z^5 - 3671888 z^6 + 533104 z^7 - 22880 z^8)) + (1/(29872128 z^(5/2))) (Sqrt[Pi] (765765 + 2187900 z + 8508500 z^2 - 18564000 z^3 + 7854000 z^4 - 1089088 z^5 + 45760 z^6) Erfi[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]