Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.8101)

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=9/2

http://functions.wolfram.com/07.25.03.8101.01

Input Form

HypergeometricPFQ[{-(7/2), 5}, {9/2, 6}, -z] == 280/(7293 z^5) + (1/(179232768 z^5)) ((-6881280 - 6881280 z + 15703485 z^2 - 20546260 z^3 + 29322860 z^4 + 83569056 z^5 + 31183856 z^6 + 3743168 z^7 + 137280 z^8)/E^z) + (1/(358465536 z^(7/2))) (Sqrt[Pi] (-19144125 + 32162130 z - 45945900 z^2 + 119119000 z^3 + 194922000 z^4 + 65973600 z^5 + 7623616 z^6 + 274560 z^7) 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]