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

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(7/2), 4}, z] == (1/(31255875 z)) (4 E^(z/2) (1216215 + 7790580 z - 20241900 z^2 + 35267400 z^3 - 70761600 z^4 + 331382016 z^5 + 1244097792 z^6 + 1062858240 z^7 + 379392768 z^8 + 66210816 z^9 + 5876736 z^10 + 251904 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/(31255875 z^2)) (4 E^(z/2) (-4864860 + 93555 z - 2347380 z^2 + 8788500 z^3 - 15762600 z^4 + 27107136 z^5 - 66624768 z^6 + 591660288 z^7 + 767024640 z^8 + 321273600 z^9 + 60699648 z^10 + 5630976 z^11 + 247808 z^12 + 4096 z^13) 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]