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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(9/2), 9/2}, -z] == (1/(6480 z^3)) (-1814400 - 831600 z - 257040 z^2 - 59400 z^3 - 9000 z^4 + 630 z^5 + 1890 z^6 + 2433 z^7 + 7584 z^8 - 3600 z^9 + 448 z^10 - 16 z^11) + (1/(12960 z^(7/2))) ((Sqrt[Pi] (1814400 + 2041200 z + 1134000 z^2 + 415800 z^3 + 113400 z^4 + 24570 z^5 + 4410 z^6 + 675 z^7 + 90 z^8 - 18360 z^9 + 7632 z^10 - 912 z^11 + 32 z^12) 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]