Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5338)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=5, b₁=4

http://functions.wolfram.com/07.25.03.5338.01

Input Form

HypergeometricPFQ[{-(9/2), 5}, {4, 6}, z] == -((1/(43648605 z^3)) (8 E^(z/2) (22680 - 11340 z - 72765 z^2 - 5609520 z^3 + 7461720 z^4 - 3176448 z^5 + 559344 z^6 - 41856 z^7 + 1088 z^8) BesselI[0, z/2])) + (1/(43648605 z^4)) (8 E^(z/2) (90720 - 45360 z - 288225 z^2 - 615195 z^3 - 1534680 z^4 + 5007288 z^5 - 2676624 z^6 + 519120 z^7 - 40768 z^8 + 1088 z^9) BesselI[1, z/2])

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]