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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(11/2), 6}, z] == (1/(9823275 z^3)) (32 E^(z/2) (109994484600 - 56961429525 z + 18194576400 z^2 - 4329101700 z^3 + 827026200 z^4 - 132315120 z^5 + 18204480 z^6 - 2177280 z^7 + 207360 z^8 + 49920 z^9 + 141312 z^10 + 33792 z^11 + 2048 z^12) BesselI[0, z/2]) + (1/(9823275 z^4)) (32 E^(z/2) (-439977938400 + 227845718100 z - 86527616175 z^2 + 24437813400 z^3 - 5440535100 z^4 + 997035480 z^5 - 155146320 z^6 + 20986560 z^7 - 2522880 z^8 + 284160 z^9 - 46848 z^10 + 110592 z^11 + 31744 z^12 + 2048 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]