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

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=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(7/2), 9/2}, z] == (75600 - 31680 z + 9720 z^2 - 2304 z^3 + 390 z^4 - 81 z^6 + 274 z^7 + 108 z^8 + 8 z^9)/(144 z^3) + (1/(288 z^(7/2))) (E^z Sqrt[Pi] (-75600 + 82080 z - 44280 z^2 + 15840 z^3 - 4230 z^4 + 900 z^5 - 159 z^6 + 24 z^7 + 648 z^8 + 224 z^9 + 16 z^10) 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]