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

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=5, b₁>=-11/2

For fixed z and a₁=5/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(9/2), 11/2}, z] == (1/(144 z^4)) (-19051200 + 6955200 z - 2129400 z^2 + 521640 z^3 - 104724 z^4 + 17700 z^5 - 2565 z^6 + 315 z^7 - 22 z^8 - 36 z^9 - 8 z^10) + (1/(288 z^(9/2))) (E^z Sqrt[Pi] (19051200 - 19656000 z + 10153080 z^2 - 3500280 z^3 + 905940 z^4 - 187740 z^5 + 32445 z^6 - 4809 z^7 + 624 z^8 - 72 z^9 - 80 z^10 - 16 z^11) Erf[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]