Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0988)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=5

http://functions.wolfram.com/07.22.03.0988.01

Input Form

HypergeometricPFQ[{-(9/2)}, {5, 5}, -z] == (512 (2 Sqrt[z] (-97692469875 + 207728841600 z - 162889631100 z^2 + 248432410800 z^3 + 108086983200 z^4 + 9328343040 z^5 + 263176704 z^6 + 2666496 z^7 + 8192 z^8) BesselJ[0, Sqrt[z]]^2 - (-390769879500 + 652341877425 z - 468792878400 z^2 + 361519653600 z^3 + 203017752000 z^4 + 18270754560 z^5 + 522381312 z^6 + 5320704 z^7 + 16384 z^8) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + Sqrt[z] (-454839447825 + 626044545000 z - 456914115000 z^2 + 401289033600 z^3 + 207224366400 z^4 + 18397458432 z^5 + 523699200 z^6 + 5324800 z^7 + 16384 z^8) BesselJ[1, Sqrt[z]]^2))/ (131939107925625 z^(7/2))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]