Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8511)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8511.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 13/4}, -z] == (Sqrt[Pi] z^(9/4) (1275274794098930625 - 2511310363764048000 z + 8272551786516864000 z^2 + 4201931066167296000 z^3 + 480220693276262400 z^4 + 19269043491962880 z^5 + 311418884718592 z^6 + 2025077080064 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (65643912069120000 + 110031700230144000 z - 230973930096473025 z^2 + 350589070104966000 z^3 + 238349262898010880 z^4 + 28952561607782400 z^5 + 1186526373150720 z^6 + 19346014339072 z^7 + 126315659264 z^8 + 268435456 z^9) Cos[2 Sqrt[z]] + 4 (8205489008640000 + 2813310517248000 z + 109281484092211200 z^2 - 195087075991471125 z^3 + 477575132324598000 z^4 + 257441414168252160 z^5 + 29795654471331840 z^6 + 1200717009321984 z^7 + 19440059023360 z^8 + 126516985856 z^9 + 268435456 z^10) Sin[2 Sqrt[z]]))/(7535945064225177600 z^(9/2))

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]