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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(11/2), 5}, z] == (1/(343814625 z^2)) (32 E^(z/2) (1964187225 - 930404475 z + 297504900 z^2 - 79209900 z^3 + 21772800 z^4 - 8255520 z^5 + 5080320 z^6 - 5287680 z^7 + 15033600 z^8 + 36215040 z^9 + 15916032 z^10 + 2608128 z^11 + 176128 z^12 + 4096 z^13) BesselI[0, z/2]) + (1/(343814625 z^3)) (32 E^(z/2) (-7856748900 + 3721617900 z - 1392566175 z^2 + 372972600 z^3 - 72746100 z^4 + 8074080 z^5 + 1905120 z^6 - 2557440 z^7 + 2522880 z^8 - 3855360 z^9 + 23715072 z^10 + 13559808 z^11 + 2438144 z^12 + 172032 z^13 + 4096 z^14) 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]